[{"citation":{"mla":"Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” <i>Nonlinearity</i>, vol. 36, no. 8, IOP Publishing, 2023, pp. 4438–69, doi:<a href=\"https://doi.org/10.1088/1361-6544/ace22e\">10.1088/1361-6544/ace22e</a>.","bibtex":"@article{Winkler_2023, title={Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction}, volume={36}, DOI={<a href=\"https://doi.org/10.1088/1361-6544/ace22e\">10.1088/1361-6544/ace22e</a>}, number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Winkler, Michael}, year={2023}, pages={4438–4469} }","ama":"Winkler M. Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. <i>Nonlinearity</i>. 2023;36(8):4438-4469. doi:<a href=\"https://doi.org/10.1088/1361-6544/ace22e\">10.1088/1361-6544/ace22e</a>","ieee":"M. Winkler, “Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction,” <i>Nonlinearity</i>, vol. 36, no. 8, pp. 4438–4469, 2023, doi: <a href=\"https://doi.org/10.1088/1361-6544/ace22e\">10.1088/1361-6544/ace22e</a>.","apa":"Winkler, M. (2023). Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. <i>Nonlinearity</i>, <i>36</i>(8), 4438–4469. <a href=\"https://doi.org/10.1088/1361-6544/ace22e\">https://doi.org/10.1088/1361-6544/ace22e</a>","short":"M. Winkler, Nonlinearity 36 (2023) 4438–4469.","chicago":"Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” <i>Nonlinearity</i> 36, no. 8 (2023): 4438–69. <a href=\"https://doi.org/10.1088/1361-6544/ace22e\">https://doi.org/10.1088/1361-6544/ace22e</a>."},"status":"public","_id":"63281","publisher":"IOP Publishing","page":"4438-4469","volume":36,"user_id":"31496","issue":"8","publication":"Nonlinearity","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>A no-flux initial-boundary value problem for<jats:disp-formula id=\"nonace22eueqn1\"><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" overflow=\"scroll\"><mml:mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em\" rowspacing=\"3pt\"><mml:mtr><mml:mtd><mml:mfenced close=\"\" open=\"{\"><mml:mtable columnalign=\"left left\" columnspacing=\"1em\" rowspacing=\".1em\"><mml:mtr><mml:mtd><mml:msub><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mml:mo></mml:mrow><mml:mi>u</mml:mi><mml:mi>ϕ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>v</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>v</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mi>v</mml:mi><mml:mo>−</mml:mo><mml:mi>u</mml:mi><mml:mi>v</mml:mi><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>⋆</mml:mo><mml:mo stretchy=\"false\">)</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math><jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" orientation=\"portrait\" position=\"float\" xlink:href=\"nonace22eueqn1.gif\" xlink:type=\"simple\"/></jats:disp-formula>is considered in smoothly bounded subdomains of<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn1.gif\" xlink:type=\"simple\"/></jats:inline-formula>with<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>n</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn2.gif\" xlink:type=\"simple\"/></jats:inline-formula>and suitably regular initial data, where<jats:italic>φ</jats:italic>is assumed to reflect algebraic type cross-degeneracies by sharing essential features with<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mn>0</mml:mn><mml:mo>⩽</mml:mo><mml:mi>ξ</mml:mi><mml:mo stretchy=\"false\">↦</mml:mo><mml:msup><mml:mi>ξ</mml:mi><mml:mi>α</mml:mi></mml:msup></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn3.gif\" xlink:type=\"simple\"/></jats:inline-formula>for some<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>α</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn4.gif\" xlink:type=\"simple\"/></jats:inline-formula>. Based on the discovery of a gradient structure acting at regularity levels mild enough to be consistent with degeneracy-driven limitations of smoothness information, in this general setting it is shown that with some measurable limit profile<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:msub><mml:mi>u</mml:mi><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:msub></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn5.gif\" xlink:type=\"simple\"/></jats:inline-formula>and some null set<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:msub><mml:mi>N</mml:mi><mml:mo>⋆</mml:mo></mml:msub><mml:mo>⊂</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant=\"normal\">∞</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn6.gif\" xlink:type=\"simple\"/></jats:inline-formula>, a corresponding global generalized solution, known to exist according to recent literature, satisfies<jats:disp-formula id=\"nonace22eueqn2\"><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" overflow=\"scroll\"><mml:mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em\" rowspacing=\"3pt\"><mml:mtr><mml:mtd><mml:mi>ρ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>u</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>⋅</mml:mo><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mover><mml:mrow><mml:mo stretchy=\"false\">⇀</mml:mo></mml:mrow><mml:mrow><mml:mo>⋆</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mi>ρ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mtext>in </mml:mtext></mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:msup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"normal\">Ω</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mtext> and </mml:mtext></mml:mrow><mml:mi>v</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>⋅</mml:mo><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mrow><mml:mtext>in </mml:mtext></mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"normal\">Ω</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mtext>for all </mml:mtext></mml:mrow><mml:mi>p</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:mtd></mml:mtr></mml:mtable></mml:math><jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" orientation=\"portrait\" position=\"float\" xlink:href=\"nonace22eueqn2.gif\" xlink:type=\"simple\"/></jats:disp-formula>as<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant=\"normal\">∞</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>∖</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mo>⋆</mml:mo></mml:msub><mml:mo>∋</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn7.gif\" xlink:type=\"simple\"/></jats:inline-formula>, where<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>ρ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ξ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>:=</mml:mo><mml:mfrac><mml:msup><mml:mi>ξ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ξ</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:msup><mml:mo stretchy=\"false\">)</mml:mo><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:mfrac></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn8.gif\" xlink:type=\"simple\"/></jats:inline-formula>,<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>ξ</mml:mi><mml:mo>⩾</mml:mo><mml:mn>0</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn9.gif\" xlink:type=\"simple\"/></jats:inline-formula>. In the particular case when either<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>n</mml:mi><mml:mo>⩽</mml:mo><mml:mn>2</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn10.gif\" xlink:type=\"simple\"/></jats:inline-formula>and<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>α</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn11.gif\" xlink:type=\"simple\"/></jats:inline-formula>is arbitrary, or<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>n</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn12.gif\" xlink:type=\"simple\"/></jats:inline-formula>and<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>α</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn13.gif\" xlink:type=\"simple\"/></jats:inline-formula>, additional quantitative information on the deviation of trajectories from the initial data is derived. This is found to imply a lower estimate for the spatial oscillation of the respective first components throughout evolution, and moreover this is seen to entail that each of the uncountably many steady states<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mo>⋆</mml:mo></mml:msub><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn14.gif\" xlink:type=\"simple\"/></jats:inline-formula>of (<jats:inline-formula><jats:tex-math/><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mo>⋆</mml:mo></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn15.gif\" xlink:type=\"simple\"/></jats:inline-formula>) is stable with respect to a suitably chosen norm topology.</jats:p>"}],"date_created":"2025-12-18T19:17:01Z","type":"journal_article","publication_identifier":{"issn":["0951-7715","1361-6544"]},"author":[{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler","id":"31496"}],"year":"2023","title":"Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction","intvolume":"        36","date_updated":"2025-12-18T20:12:06Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1088/1361-6544/ace22e"},{"citation":{"ama":"Tian Y, Winkler M. Keller–Segel–Stokes interaction involving signal‐dependent motilities. <i>Mathematical Methods in the Applied Sciences</i>. 2023;46(14):15667-15683. doi:<a href=\"https://doi.org/10.1002/mma.9419\">10.1002/mma.9419</a>","bibtex":"@article{Tian_Winkler_2023, title={Keller–Segel–Stokes interaction involving signal‐dependent motilities}, volume={46}, DOI={<a href=\"https://doi.org/10.1002/mma.9419\">10.1002/mma.9419</a>}, number={14}, journal={Mathematical Methods in the Applied Sciences}, publisher={Wiley}, author={Tian, Yu and Winkler, Michael}, year={2023}, pages={15667–15683} }","mla":"Tian, Yu, and Michael Winkler. “Keller–Segel–Stokes Interaction Involving Signal‐dependent Motilities.” <i>Mathematical Methods in the Applied Sciences</i>, vol. 46, no. 14, Wiley, 2023, pp. 15667–83, doi:<a href=\"https://doi.org/10.1002/mma.9419\">10.1002/mma.9419</a>.","short":"Y. Tian, M. Winkler, Mathematical Methods in the Applied Sciences 46 (2023) 15667–15683.","chicago":"Tian, Yu, and Michael Winkler. “Keller–Segel–Stokes Interaction Involving Signal‐dependent Motilities.” <i>Mathematical Methods in the Applied Sciences</i> 46, no. 14 (2023): 15667–83. <a href=\"https://doi.org/10.1002/mma.9419\">https://doi.org/10.1002/mma.9419</a>.","apa":"Tian, Y., &#38; Winkler, M. (2023). Keller–Segel–Stokes interaction involving signal‐dependent motilities. <i>Mathematical Methods in the Applied Sciences</i>, <i>46</i>(14), 15667–15683. <a href=\"https://doi.org/10.1002/mma.9419\">https://doi.org/10.1002/mma.9419</a>","ieee":"Y. Tian and M. Winkler, “Keller–Segel–Stokes interaction involving signal‐dependent motilities,” <i>Mathematical Methods in the Applied Sciences</i>, vol. 46, no. 14, pp. 15667–15683, 2023, doi: <a href=\"https://doi.org/10.1002/mma.9419\">10.1002/mma.9419</a>."},"status":"public","user_id":"31496","volume":46,"page":"15667-15683","_id":"63276","publisher":"Wiley","abstract":[{"text":"<jats:p>The chemotaxis‐Stokes system \r\n<jats:disp-formula>\r\n\r\n</jats:disp-formula>is considered along with homogeneous boundary conditions of no‐flux type for \r\n and \r\n, and of Dirichlet type for \r\n, in a smoothly bounded domain \r\n. Under the assumption that \r\n, that \r\n is bounded on each of the intervals \r\n with arbitrary \r\n, and that with some \r\n and \r\n, we have \r\n<jats:disp-formula>\r\n\r\n</jats:disp-formula>It is shown that for any suitably regular initial data, an associated initial‐boundary value problem admits a global very weak solution.</jats:p>","lang":"eng"}],"publication":"Mathematical Methods in the Applied Sciences","issue":"14","type":"journal_article","date_created":"2025-12-18T19:15:06Z","publication_status":"published","date_updated":"2025-12-18T20:11:29Z","intvolume":"        46","title":"Keller–Segel–Stokes interaction involving signal‐dependent motilities","year":"2023","publication_identifier":{"issn":["0170-4214","1099-1476"]},"author":[{"first_name":"Yu","last_name":"Tian","full_name":"Tian, Yu"},{"id":"31496","full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"doi":"10.1002/mma.9419","language":[{"iso":"eng"}]},{"volume":12,"user_id":"31496","doi":"10.3934/eect.2023031","_id":"63275","publisher":"American Institute of Mathematical Sciences (AIMS)","language":[{"iso":"eng"}],"page":"1676-1687","intvolume":"        12","publication_status":"published","date_updated":"2025-12-18T20:11:23Z","author":[{"full_name":"Tao, Youshan","last_name":"Tao","first_name":"Youshan"},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler","id":"31496"}],"publication_identifier":{"issn":["2163-2480"]},"title":"Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities","year":"2023","status":"public","type":"journal_article","date_created":"2025-12-18T19:14:46Z","citation":{"mla":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” <i>Evolution Equations and Control Theory</i>, vol. 12, no. 6, American Institute of Mathematical Sciences (AIMS), 2023, pp. 1676–87, doi:<a href=\"https://doi.org/10.3934/eect.2023031\">10.3934/eect.2023031</a>.","apa":"Tao, Y., &#38; Winkler, M. (2023). Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities. <i>Evolution Equations and Control Theory</i>, <i>12</i>(6), 1676–1687. <a href=\"https://doi.org/10.3934/eect.2023031\">https://doi.org/10.3934/eect.2023031</a>","ieee":"Y. Tao and M. Winkler, “Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities,” <i>Evolution Equations and Control Theory</i>, vol. 12, no. 6, pp. 1676–1687, 2023, doi: <a href=\"https://doi.org/10.3934/eect.2023031\">10.3934/eect.2023031</a>.","short":"Y. Tao, M. Winkler, Evolution Equations and Control Theory 12 (2023) 1676–1687.","ama":"Tao Y, Winkler M. Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities. <i>Evolution Equations and Control Theory</i>. 2023;12(6):1676-1687. doi:<a href=\"https://doi.org/10.3934/eect.2023031\">10.3934/eect.2023031</a>","chicago":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” <i>Evolution Equations and Control Theory</i> 12, no. 6 (2023): 1676–87. <a href=\"https://doi.org/10.3934/eect.2023031\">https://doi.org/10.3934/eect.2023031</a>.","bibtex":"@article{Tao_Winkler_2023, title={Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities}, volume={12}, DOI={<a href=\"https://doi.org/10.3934/eect.2023031\">10.3934/eect.2023031</a>}, number={6}, journal={Evolution Equations and Control Theory}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Tao, Youshan and Winkler, Michael}, year={2023}, pages={1676–1687} }"},"publication":"Evolution Equations and Control Theory","issue":"6"},{"citation":{"apa":"Painter, K. J., &#38; Winkler, M. (2023). Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. <i>SIAM Journal on Applied Mathematics</i>, <i>83</i>(5), 2096–2117. <a href=\"https://doi.org/10.1137/22m1539393\">https://doi.org/10.1137/22m1539393</a>","ieee":"K. J. Painter and M. Winkler, “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities,” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 5, pp. 2096–2117, 2023, doi: <a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>.","chicago":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” <i>SIAM Journal on Applied Mathematics</i> 83, no. 5 (2023): 2096–2117. <a href=\"https://doi.org/10.1137/22m1539393\">https://doi.org/10.1137/22m1539393</a>.","short":"K.J. Painter, M. Winkler, SIAM Journal on Applied Mathematics 83 (2023) 2096–2117.","mla":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 5, Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 2096–117, doi:<a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>.","ama":"Painter KJ, Winkler M. Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. <i>SIAM Journal on Applied Mathematics</i>. 2023;83(5):2096-2117. doi:<a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>","bibtex":"@article{Painter_Winkler_2023, title={Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}, volume={83}, DOI={<a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>}, number={5}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Painter, Kevin J. and Winkler, Michael}, year={2023}, pages={2096–2117} }"},"publication":"SIAM Journal on Applied Mathematics","issue":"5","date_created":"2025-12-18T19:15:29Z","type":"journal_article","publication_identifier":{"issn":["0036-1399","1095-712X"]},"author":[{"full_name":"Painter, Kevin J.","last_name":"Painter","first_name":"Kevin J."},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler","id":"31496"}],"year":"2023","status":"public","title":"Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities","intvolume":"        83","publication_status":"published","date_updated":"2025-12-18T20:11:36Z","publisher":"Society for Industrial & Applied Mathematics (SIAM)","_id":"63277","language":[{"iso":"eng"}],"page":"2096-2117","volume":83,"user_id":"31496","doi":"10.1137/22m1539393"},{"citation":{"ieee":"M. Winkler, “Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction,” <i>Zeitschrift für angewandte Mathematik und Physik</i>, vol. 74, no. 1, Art. no. 32, 2023, doi: <a href=\"https://doi.org/10.1007/s00033-022-01925-3\">10.1007/s00033-022-01925-3</a>.","apa":"Winkler, M. (2023). Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction. <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, <i>74</i>(1), Article 32. <a href=\"https://doi.org/10.1007/s00033-022-01925-3\">https://doi.org/10.1007/s00033-022-01925-3</a>","mla":"Winkler, Michael. “Global Generalized Solvability in a Strongly Degenerate Taxis-Type Parabolic System Modeling Migration–Consumption Interaction.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, vol. 74, no. 1, 32, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s00033-022-01925-3\">10.1007/s00033-022-01925-3</a>.","bibtex":"@article{Winkler_2023, title={Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction}, volume={74}, DOI={<a href=\"https://doi.org/10.1007/s00033-022-01925-3\">10.1007/s00033-022-01925-3</a>}, number={132}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2023} }","chicago":"Winkler, Michael. “Global Generalized Solvability in a Strongly Degenerate Taxis-Type Parabolic System Modeling Migration–Consumption Interaction.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i> 74, no. 1 (2023). <a href=\"https://doi.org/10.1007/s00033-022-01925-3\">https://doi.org/10.1007/s00033-022-01925-3</a>.","short":"M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 74 (2023).","ama":"Winkler M. Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction. <i>Zeitschrift für angewandte Mathematik und Physik</i>. 2023;74(1). doi:<a href=\"https://doi.org/10.1007/s00033-022-01925-3\">10.1007/s00033-022-01925-3</a>"},"user_id":"31496","volume":74,"_id":"63283","publisher":"Springer Science and Business Media LLC","status":"public","type":"journal_article","date_created":"2025-12-18T19:17:51Z","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>The parabolic problem <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t=\\Delta \\big (u\\phi (v)\\big ), \\\\ v_t=\\Delta v-uv, \\end{array} \\right. \\end{aligned}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:mfenced>\r\n                            <mml:mrow>\r\n                              <mml:mtable>\r\n                                <mml:mtr>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:msub>\r\n                                        <mml:mi>u</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n                                      <mml:mo>=</mml:mo>\r\n                                      <mml:mi>Δ</mml:mi>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mi>u</mml:mi>\r\n                                      <mml:mi>ϕ</mml:mi>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n                                        <mml:mi>v</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                </mml:mtr>\r\n                                <mml:mtr>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:mrow/>\r\n                                      <mml:msub>\r\n                                        <mml:mi>v</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n                                      <mml:mo>=</mml:mo>\r\n                                      <mml:mi>Δ</mml:mi>\r\n                                      <mml:mi>v</mml:mi>\r\n                                      <mml:mo>-</mml:mo>\r\n                                      <mml:mi>u</mml:mi>\r\n                                      <mml:mi>v</mml:mi>\r\n                                      <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                </mml:mtr>\r\n                              </mml:mtable>\r\n                            </mml:mrow>\r\n                          </mml:mfenced>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula>is considered in smoothly bounded subdomains of <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbb {R}}^n$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n                    <mml:mrow>\r\n                      <mml:mi>R</mml:mi>\r\n                    </mml:mrow>\r\n                    <mml:mi>n</mml:mi>\r\n                  </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with arbitrary <jats:inline-formula><jats:alternatives><jats:tex-math>$$n\\ge 1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. Under the assumptions that <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\phi \\in C^0([0,\\infty )) \\cap C^3((0,\\infty ))$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>ϕ</mml:mi>\r\n                    <mml:mo>∈</mml:mo>\r\n                    <mml:msup>\r\n                      <mml:mi>C</mml:mi>\r\n                      <mml:mn>0</mml:mn>\r\n                    </mml:msup>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mrow>\r\n                        <mml:mo>[</mml:mo>\r\n                        <mml:mn>0</mml:mn>\r\n                        <mml:mo>,</mml:mo>\r\n                        <mml:mi>∞</mml:mi>\r\n                        <mml:mo>)</mml:mo>\r\n                      </mml:mrow>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                    <mml:mo>∩</mml:mo>\r\n                    <mml:msup>\r\n                      <mml:mi>C</mml:mi>\r\n                      <mml:mn>3</mml:mn>\r\n                    </mml:msup>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mrow>\r\n                        <mml:mo>(</mml:mo>\r\n                        <mml:mn>0</mml:mn>\r\n                        <mml:mo>,</mml:mo>\r\n                        <mml:mi>∞</mml:mi>\r\n                        <mml:mo>)</mml:mo>\r\n                      </mml:mrow>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> is positive on <jats:inline-formula><jats:alternatives><jats:tex-math>$$(0,\\infty )$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                    <mml:mo>,</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n                    <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> and satisfies <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\liminf _{\\xi \\searrow 0} \\frac{\\phi (\\xi )}{\\xi ^\\alpha }&gt;0 \\quad {\\text{ and }} \\quad \\limsup _{\\xi \\searrow 0} \\big \\{ \\xi ^\\beta |\\phi '(\\xi )| \\big \\}&lt;\\infty \\end{aligned}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:mrow>\r\n                            <mml:munder>\r\n                              <mml:mo>lim inf</mml:mo>\r\n                              <mml:mrow>\r\n                                <mml:mi>ξ</mml:mi>\r\n                                <mml:mo>↘</mml:mo>\r\n                                <mml:mn>0</mml:mn>\r\n                              </mml:mrow>\r\n                            </mml:munder>\r\n                            <mml:mfrac>\r\n                              <mml:mrow>\r\n                                <mml:mi>ϕ</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>ξ</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n                              <mml:msup>\r\n                                <mml:mi>ξ</mml:mi>\r\n                                <mml:mi>α</mml:mi>\r\n                              </mml:msup>\r\n                            </mml:mfrac>\r\n                            <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n                            <mml:mspace/>\r\n                            <mml:mrow>\r\n                              <mml:mspace/>\r\n                              <mml:mtext>and</mml:mtext>\r\n                              <mml:mspace/>\r\n                            </mml:mrow>\r\n                            <mml:mspace/>\r\n                            <mml:munder>\r\n                              <mml:mo>lim sup</mml:mo>\r\n                              <mml:mrow>\r\n                                <mml:mi>ξ</mml:mi>\r\n                                <mml:mo>↘</mml:mo>\r\n                                <mml:mn>0</mml:mn>\r\n                              </mml:mrow>\r\n                            </mml:munder>\r\n                            <mml:mrow>\r\n                              <mml:mo>{</mml:mo>\r\n                            </mml:mrow>\r\n                            <mml:msup>\r\n                              <mml:mi>ξ</mml:mi>\r\n                              <mml:mi>β</mml:mi>\r\n                            </mml:msup>\r\n                            <mml:mrow>\r\n                              <mml:mo>|</mml:mo>\r\n                              <mml:msup>\r\n                                <mml:mi>ϕ</mml:mi>\r\n                                <mml:mo>′</mml:mo>\r\n                              </mml:msup>\r\n                              <mml:mrow>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>ξ</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n                              <mml:mo>|</mml:mo>\r\n                            </mml:mrow>\r\n                            <mml:mrow>\r\n                              <mml:mo>}</mml:mo>\r\n                            </mml:mrow>\r\n                            <mml:mo>&lt;</mml:mo>\r\n                            <mml:mi>∞</mml:mi>\r\n                          </mml:mrow>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula>with some <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha &gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>α</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta &gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>β</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, for all reasonably regular initial data an associated no-flux type initial-boundary value problem is shown to admit a global solution in an appropriately generalized sense. This extends previously developed solution theories on problems of this form, which either concentrated on non-degenerate or weakly degenerate cases corresponding to the choices <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha =0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>α</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha \\in (0,2)$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>α</mml:mi>\r\n                    <mml:mo>∈</mml:mo>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                    <mml:mo>,</mml:mo>\r\n                    <mml:mn>2</mml:mn>\r\n                    <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, or were restricted to low-dimensional settings by requiring that <jats:inline-formula><jats:alternatives><jats:tex-math>$$n\\le 2$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mo>≤</mml:mo>\r\n                    <mml:mn>2</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>.</jats:p>","lang":"eng"}],"publication":"Zeitschrift für angewandte Mathematik und Physik","issue":"1","doi":"10.1007/s00033-022-01925-3","article_number":"32","language":[{"iso":"eng"}],"date_updated":"2025-12-18T20:12:20Z","publication_status":"published","intvolume":"        74","title":"Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction","year":"2023","publication_identifier":{"issn":["0044-2275","1420-9039"]},"author":[{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael","id":"31496"}]},{"citation":{"chicago":"Li, Genglin, and Michael Winkler. “Refined Regularity Analysis for a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” <i>Applicable Analysis</i> 103, no. 1 (2023): 45–64. <a href=\"https://doi.org/10.1080/00036811.2023.2173183\">https://doi.org/10.1080/00036811.2023.2173183</a>.","ama":"Li G, Winkler M. Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities. <i>Applicable Analysis</i>. 2023;103(1):45-64. doi:<a href=\"https://doi.org/10.1080/00036811.2023.2173183\">10.1080/00036811.2023.2173183</a>","short":"G. Li, M. Winkler, Applicable Analysis 103 (2023) 45–64.","bibtex":"@article{Li_Winkler_2023, title={Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities}, volume={103}, DOI={<a href=\"https://doi.org/10.1080/00036811.2023.2173183\">10.1080/00036811.2023.2173183</a>}, number={1}, journal={Applicable Analysis}, publisher={Informa UK Limited}, author={Li, Genglin and Winkler, Michael}, year={2023}, pages={45–64} }","apa":"Li, G., &#38; Winkler, M. (2023). Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities. <i>Applicable Analysis</i>, <i>103</i>(1), 45–64. <a href=\"https://doi.org/10.1080/00036811.2023.2173183\">https://doi.org/10.1080/00036811.2023.2173183</a>","mla":"Li, Genglin, and Michael Winkler. “Refined Regularity Analysis for a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” <i>Applicable Analysis</i>, vol. 103, no. 1, Informa UK Limited, 2023, pp. 45–64, doi:<a href=\"https://doi.org/10.1080/00036811.2023.2173183\">10.1080/00036811.2023.2173183</a>.","ieee":"G. Li and M. Winkler, “Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities,” <i>Applicable Analysis</i>, vol. 103, no. 1, pp. 45–64, 2023, doi: <a href=\"https://doi.org/10.1080/00036811.2023.2173183\">10.1080/00036811.2023.2173183</a>."},"issue":"1","publication":"Applicable Analysis","date_created":"2025-12-18T19:05:34Z","type":"journal_article","author":[{"first_name":"Genglin","last_name":"Li","full_name":"Li, Genglin"},{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael","id":"31496"}],"publication_identifier":{"issn":["0003-6811","1563-504X"]},"status":"public","title":"Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities","year":"2023","intvolume":"       103","publication_status":"published","date_updated":"2025-12-18T20:14:04Z","publisher":"Informa UK Limited","_id":"63255","language":[{"iso":"eng"}],"page":"45-64","volume":103,"user_id":"31496","doi":"10.1080/00036811.2023.2173183"},{"abstract":[{"lang":"eng","text":"<jats:p>\r\n            The taxis-type migration–consumption model accounting for signal-dependent motilities, as given by \r\n            <jats:inline-formula>\r\n              <jats:tex-math>u_{t} = \\Delta (u\\phi(v))</jats:tex-math>\r\n            </jats:inline-formula>\r\n            , \r\n            <jats:inline-formula>\r\n              <jats:tex-math>v_{t} = \\Delta v-uv</jats:tex-math>\r\n            </jats:inline-formula>\r\n            , is considered for suitably smooth functions \r\n            <jats:inline-formula>\r\n              <jats:tex-math>\\phi\\colon[0,\\infty)\\to\\R</jats:tex-math>\r\n            </jats:inline-formula>\r\n             which are such that \r\n            <jats:inline-formula>\r\n              <jats:tex-math>\\phi&gt;0</jats:tex-math>\r\n            </jats:inline-formula>\r\n             on \r\n            <jats:inline-formula>\r\n              <jats:tex-math>(0,\\infty)</jats:tex-math>\r\n            </jats:inline-formula>\r\n            , but that in addition \r\n            <jats:inline-formula>\r\n              <jats:tex-math>\\phi(0)=0</jats:tex-math>\r\n            </jats:inline-formula>\r\n             with \r\n            <jats:inline-formula>\r\n              <jats:tex-math>\\phi'(0)&gt;0</jats:tex-math>\r\n            </jats:inline-formula>\r\n            . In order to appropriately cope with the diffusion degeneracies thereby included, this study separately examines the Neumann problem for the linear equation \r\n            <jats:inline-formula>\r\n              <jats:tex-math>V_{t} = \\Delta V + \\nabla\\cdot ( a(x,t)V) + b(x,t)V</jats:tex-math>\r\n            </jats:inline-formula>\r\n             and establishes a statement on how pointwise positive lower bounds for nonnegative solutions depend on the supremum and the mass of the initial data, and on integrability features of \r\n            <jats:inline-formula>\r\n              <jats:tex-math>a</jats:tex-math>\r\n            </jats:inline-formula>\r\n             and \r\n            <jats:inline-formula>\r\n              <jats:tex-math>b</jats:tex-math>\r\n            </jats:inline-formula>\r\n            . This is thereafter used as a key tool in the derivation of a result on global existence of solutions to the equation above, smooth and classical for positive times, under the mere assumption that the suitably regular initial data be nonnegative in both components. Apart from that, these solutions are seen to stabilize toward some equilibrium, and as a qualitative effect genuinely due to degeneracy in diffusion, a criterion on initial smallness of the second component is identified as sufficient for this limit state to be spatially nonconstant.\r\n          </jats:p>"}],"publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","issue":"1","type":"journal_article","date_created":"2025-12-18T19:08:10Z","intvolume":"        41","publication_status":"published","date_updated":"2025-12-18T20:14:52Z","publication_identifier":{"issn":["0294-1449","1873-1430"]},"author":[{"id":"31496","full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"title":"A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion","year":"2023","doi":"10.4171/aihpc/73","language":[{"iso":"eng"}],"citation":{"ieee":"M. Winkler, “A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion,” <i>Annales de l’Institut Henri Poincaré C, Analyse non linéaire</i>, vol. 41, no. 1, pp. 95–127, 2023, doi: <a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>.","apa":"Winkler, M. (2023). A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion. <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>, <i>41</i>(1), 95–127. <a href=\"https://doi.org/10.4171/aihpc/73\">https://doi.org/10.4171/aihpc/73</a>","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 41 (2023) 95–127.","chicago":"Winkler, Michael. “A Quantitative Strong Parabolic Maximum Principle and Application to a Taxis-Type Migration–Consumption Model Involving Signal-Dependent Degenerate Diffusion.” <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i> 41, no. 1 (2023): 95–127. <a href=\"https://doi.org/10.4171/aihpc/73\">https://doi.org/10.4171/aihpc/73</a>.","mla":"Winkler, Michael. “A Quantitative Strong Parabolic Maximum Principle and Application to a Taxis-Type Migration–Consumption Model Involving Signal-Dependent Degenerate Diffusion.” <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>, vol. 41, no. 1, European Mathematical Society - EMS - Publishing House GmbH, 2023, pp. 95–127, doi:<a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>.","bibtex":"@article{Winkler_2023, title={A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion}, volume={41}, DOI={<a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>}, number={1}, journal={Annales de l’Institut Henri Poincaré C, Analyse non linéaire}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Winkler, Michael}, year={2023}, pages={95–127} }","ama":"Winkler M. A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion. <i>Annales de l’Institut Henri Poincaré C, Analyse non linéaire</i>. 2023;41(1):95-127. doi:<a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>"},"status":"public","volume":41,"user_id":"31496","_id":"63261","publisher":"European Mathematical Society - EMS - Publishing House GmbH","page":"95-127"},{"volume":151,"user_id":"31496","_id":"53338","publisher":"Wiley","page":"1197-1229","status":"public","citation":{"short":"J. Lankeit, M. Winkler, Studies in Applied Mathematics 151 (2023) 1197–1229.","chicago":"Lankeit, Johannes, and Michael Winkler. “Depleting the Signal: Analysis of Chemotaxis‐consumption Models—A Survey.” <i>Studies in Applied Mathematics</i> 151, no. 4 (2023): 1197–1229. <a href=\"https://doi.org/10.1111/sapm.12625\">https://doi.org/10.1111/sapm.12625</a>.","apa":"Lankeit, J., &#38; Winkler, M. (2023). Depleting the signal: Analysis of chemotaxis‐consumption models—A survey. <i>Studies in Applied Mathematics</i>, <i>151</i>(4), 1197–1229. <a href=\"https://doi.org/10.1111/sapm.12625\">https://doi.org/10.1111/sapm.12625</a>","ieee":"J. Lankeit and M. Winkler, “Depleting the signal: Analysis of chemotaxis‐consumption models—A survey,” <i>Studies in Applied Mathematics</i>, vol. 151, no. 4, pp. 1197–1229, 2023, doi: <a href=\"https://doi.org/10.1111/sapm.12625\">10.1111/sapm.12625</a>.","ama":"Lankeit J, Winkler M. Depleting the signal: Analysis of chemotaxis‐consumption models—A survey. <i>Studies in Applied Mathematics</i>. 2023;151(4):1197-1229. doi:<a href=\"https://doi.org/10.1111/sapm.12625\">10.1111/sapm.12625</a>","bibtex":"@article{Lankeit_Winkler_2023, title={Depleting the signal: Analysis of chemotaxis‐consumption models—A survey}, volume={151}, DOI={<a href=\"https://doi.org/10.1111/sapm.12625\">10.1111/sapm.12625</a>}, number={4}, journal={Studies in Applied Mathematics}, publisher={Wiley}, author={Lankeit, Johannes and Winkler, Michael}, year={2023}, pages={1197–1229} }","mla":"Lankeit, Johannes, and Michael Winkler. “Depleting the Signal: Analysis of Chemotaxis‐consumption Models—A Survey.” <i>Studies in Applied Mathematics</i>, vol. 151, no. 4, Wiley, 2023, pp. 1197–229, doi:<a href=\"https://doi.org/10.1111/sapm.12625\">10.1111/sapm.12625</a>."},"doi":"10.1111/sapm.12625","language":[{"iso":"eng"}],"intvolume":"       151","publication_status":"published","date_updated":"2025-12-18T20:16:04Z","author":[{"first_name":"Johannes","last_name":"Lankeit","full_name":"Lankeit, Johannes"},{"id":"31496","first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["0022-2526","1467-9590"]},"title":"Depleting the signal: Analysis of chemotaxis‐consumption models—A survey","year":"2023","type":"journal_article","keyword":["Applied Mathematics"],"date_created":"2024-04-07T12:50:45Z","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We give an overview of analytical results concerned with chemotaxis systems where the signal is absorbed. We recall results on existence and properties of solutions for the prototypical chemotaxis‐consumption model and various variants and review more recent findings on its ability to support the emergence of spatial structures.</jats:p>","lang":"eng"}],"issue":"4","publication":"Studies in Applied Mathematics"},{"publication":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","citation":{"ieee":"F. Colasuonno and M. Winkler, “Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\\R^n$,” <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, Art. no. 286, 2023, doi: <a href=\"https://doi.org/10.2422/2036-2145.202303_006\">10.2422/2036-2145.202303_006</a>.","apa":"Colasuonno, F., &#38; Winkler, M. (2023). Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\\R^n$. <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, Article 286. <a href=\"https://doi.org/10.2422/2036-2145.202303_006\">https://doi.org/10.2422/2036-2145.202303_006</a>","short":"F. Colasuonno, M. Winkler, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (2023).","chicago":"Colasuonno, Francesca, and Michael Winkler. “Stability vs.~instability of Singular Steady States in the Parabolic-Elliptic Keller-Segel System on $\\R^n$.” <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, 2023. <a href=\"https://doi.org/10.2422/2036-2145.202303_006\">https://doi.org/10.2422/2036-2145.202303_006</a>.","mla":"Colasuonno, Francesca, and Michael Winkler. “Stability vs.~instability of Singular Steady States in the Parabolic-Elliptic Keller-Segel System on $\\R^n$.” <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, 286, Scuola Normale Superiore - Edizioni della Normale, 2023, doi:<a href=\"https://doi.org/10.2422/2036-2145.202303_006\">10.2422/2036-2145.202303_006</a>.","bibtex":"@article{Colasuonno_Winkler_2023, title={Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\\R^n$}, DOI={<a href=\"https://doi.org/10.2422/2036-2145.202303_006\">10.2422/2036-2145.202303_006</a>}, number={286}, journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}, publisher={Scuola Normale Superiore - Edizioni della Normale}, author={Colasuonno, Francesca and Winkler, Michael}, year={2023} }","ama":"Colasuonno F, Winkler M. Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\\R^n$. <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>. Published online 2023. doi:<a href=\"https://doi.org/10.2422/2036-2145.202303_006\">10.2422/2036-2145.202303_006</a>"},"type":"journal_article","date_created":"2025-12-18T18:58:40Z","publication_status":"published","date_updated":"2025-12-18T20:17:21Z","year":"2023","status":"public","title":"Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\\R^n$","publication_identifier":{"issn":["2036-2145","0391-173X"]},"author":[{"full_name":"Colasuonno, Francesca","last_name":"Colasuonno","first_name":"Francesca"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael","id":"31496"}],"user_id":"31496","doi":"10.2422/2036-2145.202303_006","article_number":"286","publisher":"Scuola Normale Superiore - Edizioni della Normale","_id":"63243","language":[{"iso":"eng"}]},{"citation":{"mla":"Schenke, Maximilian, et al. “Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor.” <i>IEEE Transactions on Power Electronics</i>, Institute of Electrical and Electronics Engineers (IEEE), 2023, pp. 1–16, doi:<a href=\"https://doi.org/10.1109/tpel.2023.3303651\">10.1109/tpel.2023.3303651</a>.","bibtex":"@article{Schenke_Haucke-Korber_Wallscheid_2023, title={Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor}, DOI={<a href=\"https://doi.org/10.1109/tpel.2023.3303651\">10.1109/tpel.2023.3303651</a>}, journal={IEEE Transactions on Power Electronics}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Schenke, Maximilian and Haucke-Korber, Barnabas and Wallscheid, Oliver}, year={2023}, pages={1–16} }","ama":"Schenke M, Haucke-Korber B, Wallscheid O. Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor. <i>IEEE Transactions on Power Electronics</i>. Published online 2023:1-16. doi:<a href=\"https://doi.org/10.1109/tpel.2023.3303651\">10.1109/tpel.2023.3303651</a>","ieee":"M. Schenke, B. Haucke-Korber, and O. Wallscheid, “Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor,” <i>IEEE Transactions on Power Electronics</i>, pp. 1–16, 2023, doi: <a href=\"https://doi.org/10.1109/tpel.2023.3303651\">10.1109/tpel.2023.3303651</a>.","apa":"Schenke, M., Haucke-Korber, B., &#38; Wallscheid, O. (2023). Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor. <i>IEEE Transactions on Power Electronics</i>, 1–16. <a href=\"https://doi.org/10.1109/tpel.2023.3303651\">https://doi.org/10.1109/tpel.2023.3303651</a>","chicago":"Schenke, Maximilian, Barnabas Haucke-Korber, and Oliver Wallscheid. “Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor.” <i>IEEE Transactions on Power Electronics</i>, 2023, 1–16. <a href=\"https://doi.org/10.1109/tpel.2023.3303651\">https://doi.org/10.1109/tpel.2023.3303651</a>.","short":"M. Schenke, B. Haucke-Korber, O. Wallscheid, IEEE Transactions on Power Electronics (2023) 1–16."},"publication":"IEEE Transactions on Power Electronics","date_created":"2023-09-07T12:08:05Z","department":[{"_id":"52"}],"type":"journal_article","keyword":["Electrical and Electronic Engineering"],"publication_identifier":{"issn":["0885-8993","1941-0107"]},"author":[{"id":"52638","orcid":"0000-0001-5427-9527","first_name":"Maximilian","last_name":"Schenke","full_name":"Schenke, Maximilian"},{"id":"93461","orcid":"0000-0003-0862-2069","first_name":"Barnabas","last_name":"Haucke-Korber","full_name":"Haucke-Korber, Barnabas"},{"id":"11291","last_name":"Wallscheid","first_name":"Oliver","orcid":"https://orcid.org/0000-0001-9362-8777","full_name":"Wallscheid, Oliver"}],"title":"Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor","year":"2023","status":"public","date_updated":"2025-12-19T12:44:23Z","publication_status":"published","language":[{"iso":"eng"}],"_id":"46863","publisher":"Institute of Electrical and Electronics Engineers (IEEE)","page":"1-16","doi":"10.1109/tpel.2023.3303651","user_id":"93461"},{"date_created":"2023-09-07T12:08:35Z","department":[{"_id":"52"}],"type":"conference","citation":{"chicago":"Haucke-Korber, Barnabas, Maximilian Schenke, and Oliver Wallscheid. “Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors.” In <i>2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC)</i>. IEEE, 2023. <a href=\"https://doi.org/10.1109/iemdc55163.2023.10239018\">https://doi.org/10.1109/iemdc55163.2023.10239018</a>.","short":"B. Haucke-Korber, M. Schenke, O. Wallscheid, in: 2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC), IEEE, 2023.","apa":"Haucke-Korber, B., Schenke, M., &#38; Wallscheid, O. (2023). Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors. <i>2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC)</i>. <a href=\"https://doi.org/10.1109/iemdc55163.2023.10239018\">https://doi.org/10.1109/iemdc55163.2023.10239018</a>","ieee":"B. Haucke-Korber, M. Schenke, and O. Wallscheid, “Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors,” 2023, doi: <a href=\"https://doi.org/10.1109/iemdc55163.2023.10239018\">10.1109/iemdc55163.2023.10239018</a>.","ama":"Haucke-Korber B, Schenke M, Wallscheid O. Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors. In: <i>2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC)</i>. IEEE; 2023. doi:<a href=\"https://doi.org/10.1109/iemdc55163.2023.10239018\">10.1109/iemdc55163.2023.10239018</a>","bibtex":"@inproceedings{Haucke-Korber_Schenke_Wallscheid_2023, title={Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors}, DOI={<a href=\"https://doi.org/10.1109/iemdc55163.2023.10239018\">10.1109/iemdc55163.2023.10239018</a>}, booktitle={2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC)}, publisher={IEEE}, author={Haucke-Korber, Barnabas and Schenke, Maximilian and Wallscheid, Oliver}, year={2023} }","mla":"Haucke-Korber, Barnabas, et al. “Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors.” <i>2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC)</i>, IEEE, 2023, doi:<a href=\"https://doi.org/10.1109/iemdc55163.2023.10239018\">10.1109/iemdc55163.2023.10239018</a>."},"publication":"2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC)","_id":"46865","publisher":"IEEE","language":[{"iso":"eng"}],"doi":"10.1109/iemdc55163.2023.10239018","user_id":"93461","author":[{"id":"93461","full_name":"Haucke-Korber, Barnabas","first_name":"Barnabas","last_name":"Haucke-Korber","orcid":"0000-0003-0862-2069"},{"full_name":"Schenke, Maximilian","last_name":"Schenke","first_name":"Maximilian","orcid":"0000-0001-5427-9527","id":"52638"},{"id":"11291","last_name":"Wallscheid","orcid":"https://orcid.org/0000-0001-9362-8777","first_name":"Oliver","full_name":"Wallscheid, Oliver"}],"status":"public","title":"Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors","year":"2023","date_updated":"2025-12-19T12:44:15Z","publication_status":"published"},{"publication_status":"published","date_updated":"2025-12-19T12:44:03Z","title":"Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives","year":"2023","status":"public","author":[{"last_name":"Book","first_name":"Felix","full_name":"Book, Felix"},{"first_name":"Arne","last_name":"Traue","full_name":"Traue, Arne"},{"full_name":"Schenke, Maximilian","first_name":"Maximilian","orcid":"0000-0001-5427-9527","last_name":"Schenke","id":"52638"},{"id":"93461","full_name":"Haucke-Korber, Barnabas","last_name":"Haucke-Korber","orcid":"0000-0003-0862-2069","first_name":"Barnabas"},{"last_name":"Wallscheid","orcid":"https://orcid.org/0000-0001-9362-8777","first_name":"Oliver","full_name":"Wallscheid, Oliver","id":"11291"}],"user_id":"93461","doi":"10.1109/iemdc55163.2023.10239044","_id":"46864","publisher":"IEEE","language":[{"iso":"eng"}],"publication":"2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC)","citation":{"apa":"Book, F., Traue, A., Schenke, M., Haucke-Korber, B., &#38; Wallscheid, O. (2023). Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives. <i>2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC)</i>. <a href=\"https://doi.org/10.1109/iemdc55163.2023.10239044\">https://doi.org/10.1109/iemdc55163.2023.10239044</a>","ieee":"F. Book, A. Traue, M. Schenke, B. Haucke-Korber, and O. Wallscheid, “Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives,” 2023, doi: <a href=\"https://doi.org/10.1109/iemdc55163.2023.10239044\">10.1109/iemdc55163.2023.10239044</a>.","short":"F. Book, A. Traue, M. Schenke, B. Haucke-Korber, O. Wallscheid, in: 2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC), IEEE, 2023.","chicago":"Book, Felix, Arne Traue, Maximilian Schenke, Barnabas Haucke-Korber, and Oliver Wallscheid. “Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives.” In <i>2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC)</i>. IEEE, 2023. <a href=\"https://doi.org/10.1109/iemdc55163.2023.10239044\">https://doi.org/10.1109/iemdc55163.2023.10239044</a>.","mla":"Book, Felix, et al. “Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives.” <i>2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC)</i>, IEEE, 2023, doi:<a href=\"https://doi.org/10.1109/iemdc55163.2023.10239044\">10.1109/iemdc55163.2023.10239044</a>.","ama":"Book F, Traue A, Schenke M, Haucke-Korber B, Wallscheid O. Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives. In: <i>2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC)</i>. IEEE; 2023. doi:<a href=\"https://doi.org/10.1109/iemdc55163.2023.10239044\">10.1109/iemdc55163.2023.10239044</a>","bibtex":"@inproceedings{Book_Traue_Schenke_Haucke-Korber_Wallscheid_2023, title={Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives}, DOI={<a href=\"https://doi.org/10.1109/iemdc55163.2023.10239044\">10.1109/iemdc55163.2023.10239044</a>}, booktitle={2023 IEEE International Electric Machines &#38;amp; Drives Conference (IEMDC)}, publisher={IEEE}, author={Book, Felix and Traue, Arne and Schenke, Maximilian and Haucke-Korber, Barnabas and Wallscheid, Oliver}, year={2023} }"},"type":"conference","department":[{"_id":"52"}],"date_created":"2023-09-07T12:08:25Z"},{"_id":"25832","language":[{"iso":"eng"}],"page":"1080-1096","volume":26,"doi":"10.1080/13670050.2021.1981821","user_id":"76026","author":[{"full_name":"Siepmann, Philipp","first_name":"Philipp","last_name":"Siepmann"},{"id":"76026","full_name":"Rumlich, Dominik","first_name":"Dominik","last_name":"Rumlich","orcid":"0000-0001-8682-450X"},{"last_name":"Matz","first_name":"Frauke","full_name":"Matz, Frauke"},{"first_name":"Ricardo","last_name":"Römhild","full_name":"Römhild, Ricardo"}],"year":"2023","title":"Attention to diversity in German CLIL classrooms: Multi-perspective research on students’ and teachers’ perceptions","status":"public","intvolume":"        26","date_updated":"2025-12-27T09:06:35Z","date_created":"2021-10-08T05:54:50Z","department":[{"_id":"36"},{"_id":"1"},{"_id":"612"}],"type":"journal_article","citation":{"bibtex":"@article{Siepmann_Rumlich_Matz_Römhild_2023, title={Attention to diversity in German CLIL classrooms: Multi-perspective research on students’ and teachers’ perceptions}, volume={26}, DOI={<a href=\"https://doi.org/10.1080/13670050.2021.1981821\">10.1080/13670050.2021.1981821</a>}, number={9}, journal={International Journal of Bilingual Education and Bilingualism}, author={Siepmann, Philipp and Rumlich, Dominik and Matz, Frauke and Römhild, Ricardo}, year={2023}, pages={1080–1096} }","short":"P. 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Inverse procedure for measuring piezoelectric material parameters using a single multi-electrode sample. <i>Journal of Sensors and Sensor Systems</i>. 2023;12(1):163–173. doi:<a href=\"https://doi.org/10.5194/jsss-12-163-2023\">10.5194/jsss-12-163-2023</a>","mla":"Claes, Leander, et al. “Inverse Procedure for Measuring Piezoelectric Material Parameters Using a Single Multi-Electrode Sample.” <i>Journal of Sensors and Sensor Systems</i>, vol. 12, no. 1, 2023, pp. 163–173, doi:<a href=\"https://doi.org/10.5194/jsss-12-163-2023\">10.5194/jsss-12-163-2023</a>.","chicago":"Claes, Leander, Nadine Feldmann, Veronika Schulze, Lars Meihost, Henrik Kuhlmann, Benjamin Jurgelucks, Andrea Walther, and Bernd Henning. “Inverse Procedure for Measuring Piezoelectric Material Parameters Using a Single Multi-Electrode Sample.” <i>Journal of Sensors and Sensor Systems</i> 12, no. 1 (2023): 163–173. <a href=\"https://doi.org/10.5194/jsss-12-163-2023\">https://doi.org/10.5194/jsss-12-163-2023</a>.","short":"L. 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(2023). <i>Parameter Identification of Piezoelectrics improved by Neural Networks</i>.","ieee":"B. Jurgelucks, <i>Parameter Identification of Piezoelectrics improved by Neural Networks</i>. GAMM Annual Meeting, Dresden, 2023.","short":"B. Jurgelucks, Parameter Identification of Piezoelectrics Improved by Neural Networks, GAMM Annual Meeting, Dresden, 2023.","chicago":"Jurgelucks, Benjamin. <i>Parameter Identification of Piezoelectrics Improved by Neural Networks</i>. GAMM Annual Meeting, Dresden, 2023."}},{"type":"misc","place":"GAMM Annual Meeting, Dresden","date_created":"2023-06-05T07:30:26Z","project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"citation":{"chicago":"Kuess, Raphael. <i>Parameter Identification in Piezoelectricity Based on All-at-Once and Reduced Regularization</i>. GAMM Annual Meeting, Dresden, 2023.","short":"R. Kuess, Parameter Identification in Piezoelectricity Based on All-at-Once and Reduced Regularization, GAMM Annual Meeting, Dresden, 2023.","apa":"Kuess, R. (2023). <i>Parameter identification in piezoelectricity based on all-at-once and reduced regularization</i>.","ieee":"R. Kuess, <i>Parameter identification in piezoelectricity based on all-at-once and reduced regularization</i>. 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Kuhlmann, A.T. Meise, F. Seebauer, P. Wagner, R. Häb-Umbach, in: Speech Communication; 15th ITG Conference, 2023, pp. 121–125.","apa":"Kuhlmann, M., Meise, A. T., Seebauer, F., Wagner, P., &#38; Häb-Umbach, R. (2023). Investigating Speaker Embedding Disentanglement on Natural Read Speech. <i>Speech Communication; 15th ITG Conference</i>, 121–125.","ieee":"M. Kuhlmann, A. T. Meise, F. Seebauer, P. Wagner, and R. Häb-Umbach, “Investigating Speaker Embedding Disentanglement on Natural Read Speech,” in <i>Speech Communication; 15th ITG Conference</i>, 2023, pp. 121–125.","ama":"Kuhlmann M, Meise AT, Seebauer F, Wagner P, Häb-Umbach R. Investigating Speaker Embedding Disentanglement on Natural Read Speech. 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Visible‐light photoelectrocatalysts from abundant resources will play a key role in exploiting solar irradiation. Anionic doping via pre‐organization of precursors and further co‐polymerization creates tuneable semiconductors. Triazole derivative‐purpald, an unexplored precursor with sulfur (S) container, combined in different initial ratios with melamine during one solid‐state polycondensation with two thermal steps yields hybrid S‐doped carbon nitrides (C\r\n                    <jats:sub>3</jats:sub>\r\n                    N\r\n                    <jats:sub>4</jats:sub>\r\n                    ). The series of S‐doped/C\r\n                    <jats:sub>3</jats:sub>\r\n                    N\r\n                    <jats:sub>4</jats:sub>\r\n                    ‐based materials show enhanced optical, electronic, structural, textural, and morphological properties and exhibit higher performance in organic benzylamine photooxidation, oxygen evolution, and similar energy storage (capacitor brief investigation). 50M‐50P exhibits the highest photooxidation conversion (84 ± 3%) of benzylamine to imine at 535 nm – green light for 48 h, due to a discrete shoulder (≈700) nm, high sulfur content, preservation of crystal size, new intraband energy states, structural defects by layer distortion, and 10–16 nm pores with arbitrary depth. This work innovates by studying the concomitant relationships between: 1) the precursor decomposition while C\r\n                    <jats:sub>3</jats:sub>\r\n                    N\r\n                    <jats:sub>4</jats:sub>\r\n                    is formed, 2) the insertion of S impurities, 3) the S‐doped C\r\n                    <jats:sub>3</jats:sub>\r\n                    N\r\n                    <jats:sub>4</jats:sub>\r\n                    property‐activity relationships, and 4) combinatorial surface, bulk, structural, optical, and electronic characterization analysis. This work contributes to the development of disordered long‐visible‐light photocatalysts for solar energy conversion and storage.\r\n                  </jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"article_number":"2300099","doi":"10.1002/advs.202300099","publication_identifier":{"issn":["2198-3844","2198-3844"]},"author":[{"full_name":"Jerigova, Maria","last_name":"Jerigova","first_name":"Maria"},{"full_name":"Markushyna, Yevheniia","first_name":"Yevheniia","last_name":"Markushyna"},{"full_name":"Teixeira, Ivo F.","last_name":"Teixeira","first_name":"Ivo F."},{"full_name":"Badamdorj, Bolortuya","first_name":"Bolortuya","last_name":"Badamdorj"},{"full_name":"Isaacs, Mark","last_name":"Isaacs","first_name":"Mark"},{"first_name":"Daniel","last_name":"Cruz","full_name":"Cruz, Daniel"},{"full_name":"Lauermann, Iver","first_name":"Iver","last_name":"Lauermann"},{"full_name":"Muñoz‐Márquez, Miguel Ángel","last_name":"Muñoz‐Márquez","first_name":"Miguel Ángel"},{"full_name":"Tarakina, Nadezda V.","last_name":"Tarakina","first_name":"Nadezda V."},{"id":"98120","orcid":"https://orcid.org/0000-0002-8438-9548","last_name":"Lopez Salas","first_name":"Nieves","full_name":"Lopez Salas, Nieves"},{"full_name":"Savateev, Oleksandr","last_name":"Savateev","first_name":"Oleksandr"},{"first_name":"Pablo","last_name":"Jimenéz‐Calvo","full_name":"Jimenéz‐Calvo, Pablo"}],"title":"Green Light Photoelectrocatalysis with Sulfur‐Doped Carbon Nitride: Using Triazole‐Purpald for Enhanced Benzylamine Oxidation and Oxygen Evolution Reactions","year":"2023","intvolume":"        10","publication_status":"published","date_updated":"2026-01-08T13:11:24Z","citation":{"apa":"Jerigova, M., Markushyna, Y., Teixeira, I. F., Badamdorj, B., Isaacs, M., Cruz, D., Lauermann, I., Muñoz‐Márquez, M. Á., Tarakina, N. V., Lopez Salas, N., Savateev, O., &#38; Jimenéz‐Calvo, P. (2023). Green Light Photoelectrocatalysis with Sulfur‐Doped Carbon Nitride: Using Triazole‐Purpald for Enhanced Benzylamine Oxidation and Oxygen Evolution Reactions. <i>Advanced Science</i>, <i>10</i>(13), Article 2300099. <a href=\"https://doi.org/10.1002/advs.202300099\">https://doi.org/10.1002/advs.202300099</a>","mla":"Jerigova, Maria, et al. “Green Light Photoelectrocatalysis with Sulfur‐Doped Carbon Nitride: Using Triazole‐Purpald for Enhanced Benzylamine Oxidation and Oxygen Evolution Reactions.” <i>Advanced Science</i>, vol. 10, no. 13, 2300099, Wiley, 2023, doi:<a href=\"https://doi.org/10.1002/advs.202300099\">10.1002/advs.202300099</a>.","ieee":"M. Jerigova <i>et al.</i>, “Green Light Photoelectrocatalysis with Sulfur‐Doped Carbon Nitride: Using Triazole‐Purpald for Enhanced Benzylamine Oxidation and Oxygen Evolution Reactions,” <i>Advanced Science</i>, vol. 10, no. 13, Art. no. 2300099, 2023, doi: <a href=\"https://doi.org/10.1002/advs.202300099\">10.1002/advs.202300099</a>.","chicago":"Jerigova, Maria, Yevheniia Markushyna, Ivo F. Teixeira, Bolortuya Badamdorj, Mark Isaacs, Daniel Cruz, Iver Lauermann, et al. “Green Light Photoelectrocatalysis with Sulfur‐Doped Carbon Nitride: Using Triazole‐Purpald for Enhanced Benzylamine Oxidation and Oxygen Evolution Reactions.” <i>Advanced Science</i> 10, no. 13 (2023). <a href=\"https://doi.org/10.1002/advs.202300099\">https://doi.org/10.1002/advs.202300099</a>.","ama":"Jerigova M, Markushyna Y, Teixeira IF, et al. Green Light Photoelectrocatalysis with Sulfur‐Doped Carbon Nitride: Using Triazole‐Purpald for Enhanced Benzylamine Oxidation and Oxygen Evolution Reactions. <i>Advanced Science</i>. 2023;10(13). doi:<a href=\"https://doi.org/10.1002/advs.202300099\">10.1002/advs.202300099</a>","short":"M. Jerigova, Y. Markushyna, I.F. Teixeira, B. Badamdorj, M. Isaacs, D. Cruz, I. Lauermann, M.Á. Muñoz‐Márquez, N.V. Tarakina, N. Lopez Salas, O. Savateev, P. Jimenéz‐Calvo, Advanced Science 10 (2023).","bibtex":"@article{Jerigova_Markushyna_Teixeira_Badamdorj_Isaacs_Cruz_Lauermann_Muñoz‐Márquez_Tarakina_Lopez Salas_et al._2023, title={Green Light Photoelectrocatalysis with Sulfur‐Doped Carbon Nitride: Using Triazole‐Purpald for Enhanced Benzylamine Oxidation and Oxygen Evolution Reactions}, volume={10}, DOI={<a href=\"https://doi.org/10.1002/advs.202300099\">10.1002/advs.202300099</a>}, number={132300099}, journal={Advanced Science}, publisher={Wiley}, author={Jerigova, Maria and Markushyna, Yevheniia and Teixeira, Ivo F. and Badamdorj, Bolortuya and Isaacs, Mark and Cruz, Daniel and Lauermann, Iver and Muñoz‐Márquez, Miguel Ángel and Tarakina, Nadezda V. and Lopez Salas, Nieves and et al.}, year={2023} }"},"_id":"62675","publisher":"Wiley","volume":10,"user_id":"98120","status":"public"},{"title":"Tin (II) Chloride Salt Melts as Non‐Innocent Solvents for the Synthesis of Low‐Temperature Nanoporous Oxo‐Carbons for Nitrate Electrochemical Hydrogenation","year":"2023","author":[{"last_name":"Zheng","first_name":"Xinyue","full_name":"Zheng, Xinyue"},{"full_name":"Tian, Zhihong","last_name":"Tian","first_name":"Zhihong"},{"first_name":"Roza","last_name":"Bouchal","full_name":"Bouchal, Roza"},{"first_name":"Markus","last_name":"Antonietti","full_name":"Antonietti, Markus"},{"first_name":"Nieves","orcid":"https://orcid.org/0000-0002-8438-9548","last_name":"Lopez Salas","full_name":"Lopez Salas, Nieves","id":"98120"},{"first_name":"Mateusz","last_name":"Odziomek","full_name":"Odziomek, Mateusz"}],"publication_identifier":{"issn":["0935-9648","1521-4095"]},"publication_status":"published","date_updated":"2026-01-08T13:16:30Z","intvolume":"        36","article_number":"2311575","language":[{"iso":"eng"}],"doi":"10.1002/adma.202311575","publication":"Advanced Materials","issue":"13","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Carbonaceous electrocatalysts offer advantages over metal‐based counterparts, being cost‐effective, sustainable, and electrochemically stable. Their high surface area increases reaction kinetics, making them valuable for environmental applications involving contaminant removal. However, their rational synthesis is challenging due to the applied high temperatures and activation steps, leading to disordered materials with limited control over doping. Here, a new synthetic pathway using carbon oxide precursors and tin chloride as a p‐block metal salt melt is presented. As a result, highly porous oxygen‐rich carbon sheets (with a surface area of 1600 m<jats:sup>2</jats:sup> g<jats:sup>−1</jats:sup>) are obtained at relatively low temperatures (400 °C). Mechanistic studies reveal that Sn(II) triggers reductive deoxygenation and concomitant condensation/cross‐linking, facilitated by the Sn(II) → Sn(IV) transition. Due to their significant surface area and oxygen doping, these materials demonstrate exceptional electrocatalytic activity in the nitrate‐to‐ammonia conversion, with an ammonia yield rate of 221 mmol g<jats:sup>−1</jats:sup> h<jats:sup>−1</jats:sup> and a Faradic efficiency of 93%. These results surpass those of other carbon‐based electrocatalysts. In situ Raman studies reveal that the reaction occurs through electrochemical hydrogenation, where active hydrogen is provided by water reduction. This work contributes to the development of carbonaceous electrocatalysts with enhanced performance for sustainable environmental applications.</jats:p>"}],"date_created":"2025-11-27T13:16:06Z","type":"journal_article","status":"public","publisher":"Wiley","_id":"62671","user_id":"98120","volume":36,"citation":{"mla":"Zheng, Xinyue, et al. “Tin (II) Chloride Salt Melts as Non‐Innocent Solvents for the Synthesis of Low‐Temperature Nanoporous Oxo‐Carbons for Nitrate Electrochemical Hydrogenation.” <i>Advanced Materials</i>, vol. 36, no. 13, 2311575, Wiley, 2023, doi:<a href=\"https://doi.org/10.1002/adma.202311575\">10.1002/adma.202311575</a>.","ama":"Zheng X, Tian Z, Bouchal R, Antonietti M, Lopez Salas N, Odziomek M. Tin (II) Chloride Salt Melts as Non‐Innocent Solvents for the Synthesis of Low‐Temperature Nanoporous Oxo‐Carbons for Nitrate Electrochemical Hydrogenation. <i>Advanced Materials</i>. 2023;36(13). doi:<a href=\"https://doi.org/10.1002/adma.202311575\">10.1002/adma.202311575</a>","bibtex":"@article{Zheng_Tian_Bouchal_Antonietti_Lopez Salas_Odziomek_2023, title={Tin (II) Chloride Salt Melts as Non‐Innocent Solvents for the Synthesis of Low‐Temperature Nanoporous Oxo‐Carbons for Nitrate Electrochemical Hydrogenation}, volume={36}, DOI={<a href=\"https://doi.org/10.1002/adma.202311575\">10.1002/adma.202311575</a>}, number={132311575}, journal={Advanced Materials}, publisher={Wiley}, author={Zheng, Xinyue and Tian, Zhihong and Bouchal, Roza and Antonietti, Markus and Lopez Salas, Nieves and Odziomek, Mateusz}, year={2023} }","apa":"Zheng, X., Tian, Z., Bouchal, R., Antonietti, M., Lopez Salas, N., &#38; Odziomek, M. (2023). Tin (II) Chloride Salt Melts as Non‐Innocent Solvents for the Synthesis of Low‐Temperature Nanoporous Oxo‐Carbons for Nitrate Electrochemical Hydrogenation. <i>Advanced Materials</i>, <i>36</i>(13), Article 2311575. <a href=\"https://doi.org/10.1002/adma.202311575\">https://doi.org/10.1002/adma.202311575</a>","ieee":"X. Zheng, Z. Tian, R. Bouchal, M. Antonietti, N. Lopez Salas, and M. Odziomek, “Tin (II) Chloride Salt Melts as Non‐Innocent Solvents for the Synthesis of Low‐Temperature Nanoporous Oxo‐Carbons for Nitrate Electrochemical Hydrogenation,” <i>Advanced Materials</i>, vol. 36, no. 13, Art. no. 2311575, 2023, doi: <a href=\"https://doi.org/10.1002/adma.202311575\">10.1002/adma.202311575</a>.","short":"X. Zheng, Z. Tian, R. Bouchal, M. Antonietti, N. Lopez Salas, M. Odziomek, Advanced Materials 36 (2023).","chicago":"Zheng, Xinyue, Zhihong Tian, Roza Bouchal, Markus Antonietti, Nieves Lopez Salas, and Mateusz Odziomek. “Tin (II) Chloride Salt Melts as Non‐Innocent Solvents for the Synthesis of Low‐Temperature Nanoporous Oxo‐Carbons for Nitrate Electrochemical Hydrogenation.” <i>Advanced Materials</i> 36, no. 13 (2023). <a href=\"https://doi.org/10.1002/adma.202311575\">https://doi.org/10.1002/adma.202311575</a>."}}]
