[{"author":[{"full_name":"Tao, Youshan","last_name":"Tao","first_name":"Youshan"},{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"volume":33,"date_updated":"2024-04-07T12:43:17Z","doi":"10.1142/s0218202523500045","publication_status":"published","publication_identifier":{"issn":["0218-2025","1793-6314"]},"citation":{"apa":"Tao, Y., & Winkler, M. (2023). Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Mathematical Models and Methods in Applied Sciences, 33(01), 103–138. https://doi.org/10.1142/s0218202523500045","mla":"Tao, Youshan, and Michael Winkler. “Small-Signal Solutions to a Nonlocal Cross-Diffusion Model for Interaction of Scroungers with Rapidly Diffusing Foragers.” Mathematical Models and Methods in Applied Sciences, vol. 33, no. 01, World Scientific Pub Co Pte Ltd, 2023, pp. 103–38, doi:10.1142/s0218202523500045.","short":"Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 33 (2023) 103–138.","bibtex":"@article{Tao_Winkler_2023, title={Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers}, volume={33}, DOI={10.1142/s0218202523500045}, number={01}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Tao, Youshan and Winkler, Michael}, year={2023}, pages={103–138} }","ama":"Tao Y, Winkler M. Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Mathematical Models and Methods in Applied Sciences. 2023;33(01):103-138. doi:10.1142/s0218202523500045","ieee":"Y. Tao and M. Winkler, “Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers,” Mathematical Models and Methods in Applied Sciences, vol. 33, no. 01, pp. 103–138, 2023, doi: 10.1142/s0218202523500045.","chicago":"Tao, Youshan, and Michael Winkler. “Small-Signal Solutions to a Nonlocal Cross-Diffusion Model for Interaction of Scroungers with Rapidly Diffusing Foragers.” Mathematical Models and Methods in Applied Sciences 33, no. 01 (2023): 103–38. https://doi.org/10.1142/s0218202523500045."},"intvolume":" 33","page":"103-138","user_id":"31496","_id":"53328","type":"journal_article","status":"public","date_created":"2024-04-07T12:43:13Z","publisher":"World Scientific Pub Co Pte Ltd","title":"Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers","issue":"01","year":"2023","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Modeling and Simulation"],"publication":"Mathematical Models and Methods in Applied Sciences","abstract":[{"lang":"eng","text":" As a simplified version of a three-component taxis cascade model accounting for different migration strategies of two population groups in search of food, a two-component nonlocal nutrient taxis system is considered in a two-dimensional bounded convex domain with smooth boundary. For any given conveniently regular and biologically meaningful initial data, smallness conditions on the prescribed resource growth and on the initial nutrient signal concentration are identified which ensure the global existence of a global classical solution to the corresponding no-flux initial-boundary value problem. Moreover, under additional assumptions on the food production source these solutions are shown to be bounded, and to stabilize toward semi-trivial equilibria in the large time limit, respectively. "}]},{"title":"A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system","doi":"10.1007/s00526-023-02523-5","publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-07T12:40:06Z","author":[{"first_name":"Jaewook","full_name":"Ahn, Jaewook","last_name":"Ahn"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"date_created":"2024-04-07T12:40:02Z","volume":62,"year":"2023","citation":{"ama":"Ahn J, Winkler M. A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system. Calculus of Variations and Partial Differential Equations. 2023;62(6). doi:10.1007/s00526-023-02523-5","chicago":"Ahn, Jaewook, and Michael Winkler. “A Critical Exponent for Blow-up in a Two-Dimensional Chemotaxis-Consumption System.” Calculus of Variations and Partial Differential Equations 62, no. 6 (2023). https://doi.org/10.1007/s00526-023-02523-5.","ieee":"J. Ahn and M. Winkler, “A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system,” Calculus of Variations and Partial Differential Equations, vol. 62, no. 6, Art. no. 180, 2023, doi: 10.1007/s00526-023-02523-5.","mla":"Ahn, Jaewook, and Michael Winkler. “A Critical Exponent for Blow-up in a Two-Dimensional Chemotaxis-Consumption System.” Calculus of Variations and Partial Differential Equations, vol. 62, no. 6, 180, Springer Science and Business Media LLC, 2023, doi:10.1007/s00526-023-02523-5.","bibtex":"@article{Ahn_Winkler_2023, title={A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system}, volume={62}, DOI={10.1007/s00526-023-02523-5}, number={6180}, journal={Calculus of Variations and Partial Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Ahn, Jaewook and Winkler, Michael}, year={2023} }","short":"J. Ahn, M. Winkler, Calculus of Variations and Partial Differential Equations 62 (2023).","apa":"Ahn, J., & Winkler, M. (2023). A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system. Calculus of Variations and Partial Differential Equations, 62(6), Article 180. https://doi.org/10.1007/s00526-023-02523-5"},"intvolume":" 62","publication_status":"published","publication_identifier":{"issn":["0944-2669","1432-0835"]},"issue":"6","article_number":"180","keyword":["Applied Mathematics","Analysis"],"language":[{"iso":"eng"}],"_id":"53324","user_id":"31496","status":"public","type":"journal_article","publication":"Calculus of Variations and Partial Differential Equations"},{"type":"journal_article","publication":"Nonlinear Analysis: Real World Applications","status":"public","user_id":"31496","_id":"53329","language":[{"iso":"eng"}],"article_number":"103820","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"publication_status":"published","publication_identifier":{"issn":["1468-1218"]},"citation":{"ieee":"Y. Tao and M. Winkler, “Analysis of a chemotaxis-SIS epidemic model with unbounded infection force,” Nonlinear Analysis: Real World Applications, vol. 71, Art. no. 103820, 2023, doi: 10.1016/j.nonrwa.2022.103820.","chicago":"Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” Nonlinear Analysis: Real World Applications 71 (2023). https://doi.org/10.1016/j.nonrwa.2022.103820.","ama":"Tao Y, Winkler M. Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. Nonlinear Analysis: Real World Applications. 2023;71. doi:10.1016/j.nonrwa.2022.103820","bibtex":"@article{Tao_Winkler_2023, title={Analysis of a chemotaxis-SIS epidemic model with unbounded infection force}, volume={71}, DOI={10.1016/j.nonrwa.2022.103820}, number={103820}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Tao, Youshan and Winkler, Michael}, year={2023} }","mla":"Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” Nonlinear Analysis: Real World Applications, vol. 71, 103820, Elsevier BV, 2023, doi:10.1016/j.nonrwa.2022.103820.","short":"Y. Tao, M. Winkler, Nonlinear Analysis: Real World Applications 71 (2023).","apa":"Tao, Y., & Winkler, M. (2023). Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. Nonlinear Analysis: Real World Applications, 71, Article 103820. https://doi.org/10.1016/j.nonrwa.2022.103820"},"intvolume":" 71","year":"2023","author":[{"first_name":"Youshan","last_name":"Tao","full_name":"Tao, Youshan"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2024-04-07T12:43:49Z","volume":71,"date_updated":"2024-04-07T12:43:53Z","publisher":"Elsevier BV","doi":"10.1016/j.nonrwa.2022.103820","title":"Analysis of a chemotaxis-SIS epidemic model with unbounded infection force"},{"_id":"53326","user_id":"31496","keyword":["Applied Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"publication":"Communications in Mathematical Sciences","type":"journal_article","status":"public","publisher":"International Press of Boston","date_updated":"2024-04-07T12:41:54Z","volume":21,"date_created":"2024-04-07T12:41:49Z","author":[{"full_name":"Li, Genglin","last_name":"Li","first_name":"Genglin"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"title":"Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities","doi":"10.4310/cms.2023.v21.n2.a1","publication_identifier":{"issn":["1539-6746","1945-0796"]},"publication_status":"published","issue":"2","year":"2023","intvolume":" 21","page":"299-322","citation":{"apa":"Li, G., & Winkler, M. (2023). Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Communications in Mathematical Sciences, 21(2), 299–322. https://doi.org/10.4310/cms.2023.v21.n2.a1","short":"G. Li, M. Winkler, Communications in Mathematical Sciences 21 (2023) 299–322.","mla":"Li, Genglin, and Michael Winkler. “Relaxation in a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Communications in Mathematical Sciences, vol. 21, no. 2, International Press of Boston, 2023, pp. 299–322, doi:10.4310/cms.2023.v21.n2.a1.","bibtex":"@article{Li_Winkler_2023, title={Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities}, volume={21}, DOI={10.4310/cms.2023.v21.n2.a1}, number={2}, journal={Communications in Mathematical Sciences}, publisher={International Press of Boston}, author={Li, Genglin and Winkler, Michael}, year={2023}, pages={299–322} }","ama":"Li G, Winkler M. Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Communications in Mathematical Sciences. 2023;21(2):299-322. doi:10.4310/cms.2023.v21.n2.a1","ieee":"G. Li and M. Winkler, “Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities,” Communications in Mathematical Sciences, vol. 21, no. 2, pp. 299–322, 2023, doi: 10.4310/cms.2023.v21.n2.a1.","chicago":"Li, Genglin, and Michael Winkler. “Relaxation in a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Communications in Mathematical Sciences 21, no. 2 (2023): 299–322. https://doi.org/10.4310/cms.2023.v21.n2.a1."}},{"abstract":[{"text":"Abstract\r\n The Cauchy problem in \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n {{\\mathbb{R}}}^{n}\r\n \r\n , \r\n \r\n \r\n \r\n n\r\n ≥\r\n 2\r\n \r\n n\\ge 2\r\n \r\n , for \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n \r\n \r\n t\r\n \r\n \r\n =\r\n Δ\r\n u\r\n −\r\n \r\n ∇\r\n \r\n ⋅\r\n \r\n (\r\n \r\n u\r\n S\r\n ⋅\r\n \r\n ∇\r\n \r\n v\r\n \r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n +\r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n (\r\n \r\n ⋆\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n \\begin{array}{r}\\left\\{\\phantom{\\rule[-1.25em]{}{0ex}}\\begin{array}{l}{u}_{t}=\\Delta u-\\nabla \\cdot \\left(uS\\cdot \\nabla v),\\\\ 0=\\Delta v+u,\\end{array}\\right.\\hspace{2.0em}\\hspace{2.0em}\\hspace{2.0em}\\left(\\star )\\end{array}\r\n \r\n is considered for general matrices \r\n \r\n \r\n \r\n S\r\n ∈\r\n \r\n \r\n R\r\n \r\n \r\n n\r\n ×\r\n n\r\n \r\n \r\n \r\n S\\in {{\\mathbb{R}}}^{n\\times n}\r\n \r\n . A theory of local-in-time classical existence and extensibility is developed in a framework that differs from those considered in large parts of the literature by involving bounded classical solutions. Specifically, it is shown that for all non-negative initial data belonging to \r\n \r\n \r\n \r\n BUC\r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n ∩\r\n \r\n \r\n L\r\n \r\n \r\n p\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n {\\rm{BUC}}\\left({{\\mathbb{R}}}^{n})\\cap {L}^{p}\\left({{\\mathbb{R}}}^{n})\r\n \r\n with some \r\n \r\n \r\n \r\n p\r\n ∈\r\n \r\n [\r\n \r\n 1\r\n ,\r\n n\r\n \r\n )\r\n \r\n \r\n p\\in \\left[1,n)\r\n \r\n , there exist \r\n \r\n \r\n \r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n ∈\r\n \r\n (\r\n \r\n 0\r\n ,\r\n ∞\r\n \r\n ]\r\n \r\n \r\n {T}_{\\max }\\in \\left(0,\\infty ]\r\n \r\n and a uniquely determined \r\n \r\n \r\n \r\n u\r\n ∈\r\n \r\n \r\n C\r\n \r\n \r\n 0\r\n \r\n \r\n \r\n (\r\n \r\n \r\n [\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n ;\r\n \r\n BUC\r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n )\r\n \r\n ∩\r\n \r\n \r\n C\r\n \r\n \r\n 0\r\n \r\n \r\n \r\n (\r\n \r\n \r\n [\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n ;\r\n \r\n \r\n \r\n L\r\n \r\n \r\n p\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n )\r\n \r\n ∩\r\n \r\n \r\n C\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n ×\r\n \r\n (\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n \r\n )\r\n \r\n \r\n u\\in {C}^{0}\\left(\\left[0,{T}_{\\max });\\hspace{0.33em}{\\rm{BUC}}\\left({{\\mathbb{R}}}^{n}))\\cap {C}^{0}\\left(\\left[0,{T}_{\\max });\\hspace{0.33em}{L}^{p}\\left({{\\mathbb{R}}}^{n}))\\cap {C}^{\\infty }\\left({{\\mathbb{R}}}^{n}\\times \\left(0,{T}_{\\max }))\r\n \r\n such that with \r\n \r\n \r\n \r\n v\r\n ≔\r\n Γ\r\n ⋆\r\n u\r\n \r\n v:= \\Gamma \\star u\r\n \r\n , and with \r\n \r\n \r\n \r\n Γ\r\n \r\n \\Gamma \r\n \r\n denoting the Newtonian kernel on \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n {{\\mathbb{R}}}^{n}\r\n \r\n , the pair \r\n \r\n \r\n \r\n \r\n (\r\n \r\n u\r\n ,\r\n v\r\n \r\n )\r\n \r\n \r\n \\left(u,v)\r\n \r\n forms a classical solution of (\r\n \r\n \r\n \r\n ⋆\r\n \r\n \\star \r\n \r\n ) in \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n ×\r\n \r\n (\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n \r\n {{\\mathbb{R}}}^{n}\\times \\left(0,{T}_{\\max })\r\n \r\n , which has the property that \r\n \r\n \r\n \r\n \r\n if\r\n \r\n \r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n <\r\n ∞\r\n ,\r\n \r\n \r\n \r\n then both\r\n \r\n \r\n \r\n \r\n \r\n limsup\r\n \r\n \r\n t\r\n ↗\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n \r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n \r\n ⋅\r\n ,\r\n t\r\n \r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n \r\n L\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n \r\n =\r\n ∞\r\n \r\n \r\n and\r\n \r\n \r\n \r\n \r\n limsup\r\n \r\n \r\n t\r\n ↗\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n \r\n \r\n \r\n ‖\r\n \r\n ∇\r\n \r\n v\r\n \r\n (\r\n \r\n ⋅\r\n ,\r\n t\r\n \r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n \r\n L\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n \r\n =\r\n ∞\r\n .\r\n \r\n \\hspace{0.1em}\\text{if}\\hspace{0.1em}\\hspace{0.33em}{T}_{\\max }\\lt \\infty ,\\hspace{1.0em}\\hspace{0.1em}\\text{then both}\\hspace{0.1em}\\hspace{0.33em}\\mathop{\\mathrm{limsup}}\\limits_{t\\nearrow {T}_{\\max }}\\Vert u\\left(\\cdot ,t){\\Vert }_{{L}^{\\infty }\\left({{\\mathbb{R}}}^{n})}=\\infty \\hspace{1.0em}\\hspace{0.1em}\\text{and}\\hspace{0.1em}\\hspace{1.0em}\\mathop{\\mathrm{limsup}}\\limits_{t\\nearrow {T}_{\\max }}\\Vert \\nabla v\\left(\\cdot ,t){\\Vert }_{{L}^{\\infty }\\left({{\\mathbb{R}}}^{n})}=\\infty .\r\n \r\n An exemplary application of this provides a result on global classical solvability in cases when \r\n \r\n \r\n \r\n ∣\r\n S\r\n +\r\n 1\r\n ∣\r\n \r\n | S+{\\bf{1}}| \r\n \r\n is sufficiently small, where \r\n \r\n \r\n \r\n 1\r\n =\r\n diag\r\n \r\n \r\n (\r\n \r\n 1\r\n ,\r\n \r\n …\r\n \r\n ,\r\n 1\r\n \r\n )\r\n \r\n \r\n {\\bf{1}}={\\rm{diag}}\\hspace{0.33em}\\left(1,\\ldots ,1)\r\n \r\n .","lang":"eng"}],"status":"public","type":"journal_article","publication":"Open Mathematics","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"_id":"53343","user_id":"31496","year":"2023","citation":{"ama":"Winkler M. Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. Open Mathematics. 2023;21(1). doi:10.1515/math-2022-0578","ieee":"M. Winkler, “Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type,” Open Mathematics, vol. 21, no. 1, 2023, doi: 10.1515/math-2022-0578.","chicago":"Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” Open Mathematics 21, no. 1 (2023). https://doi.org/10.1515/math-2022-0578.","mla":"Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” Open Mathematics, vol. 21, no. 1, Walter de Gruyter GmbH, 2023, doi:10.1515/math-2022-0578.","short":"M. Winkler, Open Mathematics 21 (2023).","bibtex":"@article{Winkler_2023, title={Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type}, volume={21}, DOI={10.1515/math-2022-0578}, number={1}, journal={Open Mathematics}, publisher={Walter de Gruyter GmbH}, author={Winkler, Michael}, year={2023} }","apa":"Winkler, M. (2023). Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. Open Mathematics, 21(1). https://doi.org/10.1515/math-2022-0578"},"intvolume":" 21","publication_status":"published","publication_identifier":{"issn":["2391-5455"]},"issue":"1","title":"Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type","doi":"10.1515/math-2022-0578","date_updated":"2024-04-07T12:54:34Z","publisher":"Walter de Gruyter GmbH","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2024-04-07T12:54:31Z","volume":21},{"year":"2023","intvolume":" 36","page":"4438-4469","citation":{"ama":"Winkler M. Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. Nonlinearity. 2023;36(8):4438-4469. doi:10.1088/1361-6544/ace22e","chicago":"Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity 36, no. 8 (2023): 4438–69. https://doi.org/10.1088/1361-6544/ace22e.","ieee":"M. Winkler, “Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction,” Nonlinearity, vol. 36, no. 8, pp. 4438–4469, 2023, doi: 10.1088/1361-6544/ace22e.","apa":"Winkler, M. (2023). Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. Nonlinearity, 36(8), 4438–4469. https://doi.org/10.1088/1361-6544/ace22e","short":"M. Winkler, Nonlinearity 36 (2023) 4438–4469.","mla":"Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity, vol. 36, no. 8, IOP Publishing, 2023, pp. 4438–69, doi:10.1088/1361-6544/ace22e.","bibtex":"@article{Winkler_2023, title={Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction}, volume={36}, DOI={10.1088/1361-6544/ace22e}, number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Winkler, Michael}, year={2023}, pages={4438–4469} }"},"publication_identifier":{"issn":["0951-7715","1361-6544"]},"publication_status":"published","issue":"8","title":"Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction","doi":"10.1088/1361-6544/ace22e","publisher":"IOP Publishing","date_updated":"2024-04-07T12:56:40Z","volume":36,"date_created":"2024-04-07T12:56:35Z","author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"abstract":[{"text":"AbstractA no-flux initial-boundary value problem forut=Δ(uϕ(v)),vt=Δv−uv,(⋆)is considered in smoothly bounded subdomains ofRnwithn⩾1and suitably regular initial data, whereφis assumed to reflect algebraic type cross-degeneracies by sharing essential features with0⩽ξ↦ξαfor someα⩾1. 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 profileu∞and some null setN⋆⊂(0,∞), a corresponding global generalized solution, known to exist according to recent literature, satisfiesρ(u(⋅,t))⇀⋆ρ(u∞)in L∞(Ω) and v(⋅,t)→0in Lp(Ω)for all p⩾1as(0,∞)∖N⋆∋t→∞, whereρ(ξ):=ξ2(ξ+1)2,ξ⩾0. In the particular case when eithern⩽2andα⩾1is arbitrary, orn⩾1andα∈[1,2], 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(u⋆,0)of (⋆) is stable with respect to a suitably chosen norm topology.","lang":"eng"}],"status":"public","publication":"Nonlinearity","type":"journal_article","keyword":["Applied Mathematics","General Physics and Astronomy","Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"_id":"53345","user_id":"31496"},{"abstract":[{"text":"AbstractThe Cauchy problem in $$\\mathbb {R}^n$$\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n is considered for the Keller–Segel system $$\\begin{aligned} \\left\\{ \\begin{array}{l}u_t = \\Delta u - \\nabla \\cdot (u\\nabla v), \\\\ 0 = \\Delta v + u, \\end{array} \\right. \\qquad \\qquad (\\star ) \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n Δ\r\n u\r\n -\r\n ∇\r\n ·\r\n \r\n (\r\n u\r\n ∇\r\n v\r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n +\r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n (\r\n ⋆\r\n )\r\n \r\n \r\n \r\n \r\n \r\n \r\n with a focus on a detailed description of behavior in the presence of nonnegative radially symmetric initial data $$u_0$$\r\n \r\n u\r\n 0\r\n \r\n with non-integrable behavior at spatial infinity. It is shown that if $$u_0$$\r\n \r\n u\r\n 0\r\n \r\n is continuous and bounded, then ($$\\star $$\r\n ⋆\r\n ) admits a local-in-time classical solution, whereas if $$u_0(x)\\rightarrow +\\infty $$\r\n \r\n \r\n u\r\n 0\r\n \r\n \r\n (\r\n x\r\n )\r\n \r\n →\r\n +\r\n ∞\r\n \r\n as $$|x|\\rightarrow \\infty $$\r\n \r\n |\r\n x\r\n |\r\n →\r\n ∞\r\n \r\n , then no such solution can be found. Furthermore, a collection of three sufficient criteria for either global existence or global nonexistence indicates that with respect to the occurrence of finite-time blow-up, spatial decay properties of an explicit singular steady state plays a critical role. In particular, this underlines that explosions in ($$\\star $$\r\n ⋆\r\n ) need not be enforced by initially high concentrations near finite points, but can be exclusively due to large tails.","lang":"eng"}],"status":"public","publication":"Journal of Elliptic and Parabolic Equations","type":"journal_article","keyword":["Applied Mathematics","Numerical Analysis","Analysis"],"language":[{"iso":"eng"}],"_id":"53341","user_id":"31496","year":"2023","intvolume":" 9","page":"919-959","citation":{"apa":"Winkler, M. (2023). Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity. Journal of Elliptic and Parabolic Equations, 9(2), 919–959. https://doi.org/10.1007/s41808-023-00230-y","mla":"Winkler, Michael. “Solutions to the Keller–Segel System with Non-Integrable Behavior at Spatial Infinity.” Journal of Elliptic and Parabolic Equations, vol. 9, no. 2, Springer Science and Business Media LLC, 2023, pp. 919–59, doi:10.1007/s41808-023-00230-y.","short":"M. Winkler, Journal of Elliptic and Parabolic Equations 9 (2023) 919–959.","bibtex":"@article{Winkler_2023, title={Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity}, volume={9}, DOI={10.1007/s41808-023-00230-y}, number={2}, journal={Journal of Elliptic and Parabolic Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2023}, pages={919–959} }","ieee":"M. Winkler, “Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity,” Journal of Elliptic and Parabolic Equations, vol. 9, no. 2, pp. 919–959, 2023, doi: 10.1007/s41808-023-00230-y.","chicago":"Winkler, Michael. “Solutions to the Keller–Segel System with Non-Integrable Behavior at Spatial Infinity.” Journal of Elliptic and Parabolic Equations 9, no. 2 (2023): 919–59. https://doi.org/10.1007/s41808-023-00230-y.","ama":"Winkler M. Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity. Journal of Elliptic and Parabolic Equations. 2023;9(2):919-959. doi:10.1007/s41808-023-00230-y"},"publication_identifier":{"issn":["2296-9020","2296-9039"]},"publication_status":"published","issue":"2","title":"Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity","doi":"10.1007/s41808-023-00230-y","date_updated":"2024-04-07T12:52:55Z","publisher":"Springer Science and Business Media LLC","volume":9,"date_created":"2024-04-07T12:52:52Z","author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}]},{"issue":"14","publication_identifier":{"issn":["0170-4214","1099-1476"]},"publication_status":"published","intvolume":" 46","page":"15667-15683","citation":{"chicago":"Tian, Yu, and Michael Winkler. “Keller–Segel–Stokes Interaction Involving Signal‐dependent Motilities.” Mathematical Methods in the Applied Sciences 46, no. 14 (2023): 15667–83. https://doi.org/10.1002/mma.9419.","ieee":"Y. Tian and M. Winkler, “Keller–Segel–Stokes interaction involving signal‐dependent motilities,” Mathematical Methods in the Applied Sciences, vol. 46, no. 14, pp. 15667–15683, 2023, doi: 10.1002/mma.9419.","ama":"Tian Y, Winkler M. Keller–Segel–Stokes interaction involving signal‐dependent motilities. Mathematical Methods in the Applied Sciences. 2023;46(14):15667-15683. doi:10.1002/mma.9419","short":"Y. Tian, M. Winkler, Mathematical Methods in the Applied Sciences 46 (2023) 15667–15683.","bibtex":"@article{Tian_Winkler_2023, title={Keller–Segel–Stokes interaction involving signal‐dependent motilities}, volume={46}, DOI={10.1002/mma.9419}, 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.” Mathematical Methods in the Applied Sciences, vol. 46, no. 14, Wiley, 2023, pp. 15667–83, doi:10.1002/mma.9419.","apa":"Tian, Y., & Winkler, M. (2023). Keller–Segel–Stokes interaction involving signal‐dependent motilities. Mathematical Methods in the Applied Sciences, 46(14), 15667–15683. https://doi.org/10.1002/mma.9419"},"year":"2023","volume":46,"author":[{"first_name":"Yu","full_name":"Tian, Yu","last_name":"Tian"},{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2024-04-07T12:51:27Z","date_updated":"2024-04-07T12:51:31Z","publisher":"Wiley","doi":"10.1002/mma.9419","title":"Keller–Segel–Stokes interaction involving signal‐dependent motilities","publication":"Mathematical Methods in the Applied Sciences","type":"journal_article","status":"public","abstract":[{"text":"The chemotaxis‐Stokes system \r\n\r\n\r\nis 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\r\n\r\nIt is shown that for any suitably regular initial data, an associated initial‐boundary value problem admits a global very weak solution.","lang":"eng"}],"user_id":"31496","_id":"53339","language":[{"iso":"eng"}],"keyword":["General Engineering","General Mathematics"]},{"title":"Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities","doi":"10.1137/22m1539393","date_updated":"2024-04-07T12:52:06Z","publisher":"Society for Industrial & Applied Mathematics (SIAM)","volume":83,"date_created":"2024-04-07T12:52:03Z","author":[{"first_name":"Kevin J.","full_name":"Painter, Kevin J.","last_name":"Painter"},{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"year":"2023","page":"2096-2117","intvolume":" 83","citation":{"ama":"Painter KJ, Winkler M. Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. SIAM Journal on Applied Mathematics. 2023;83(5):2096-2117. doi:10.1137/22m1539393","ieee":"K. J. Painter and M. Winkler, “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities,” SIAM Journal on Applied Mathematics, vol. 83, no. 5, pp. 2096–2117, 2023, doi: 10.1137/22m1539393.","chicago":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” SIAM Journal on Applied Mathematics 83, no. 5 (2023): 2096–2117. https://doi.org/10.1137/22m1539393.","apa":"Painter, K. J., & Winkler, M. (2023). Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. SIAM Journal on Applied Mathematics, 83(5), 2096–2117. https://doi.org/10.1137/22m1539393","bibtex":"@article{Painter_Winkler_2023, title={Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}, volume={83}, DOI={10.1137/22m1539393}, number={5}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Painter, Kevin J. and Winkler, Michael}, year={2023}, pages={2096–2117} }","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.” SIAM Journal on Applied Mathematics, vol. 83, no. 5, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 2096–117, doi:10.1137/22m1539393."},"publication_identifier":{"issn":["0036-1399","1095-712X"]},"publication_status":"published","issue":"5","keyword":["Applied Mathematics"],"language":[{"iso":"eng"}],"_id":"53340","user_id":"31496","status":"public","publication":"SIAM Journal on Applied Mathematics","type":"journal_article"},{"date_updated":"2024-04-07T12:53:38Z","publisher":"Elsevier BV","volume":374,"author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"},{"last_name":"Yokota","full_name":"Yokota, Tomomi","first_name":"Tomomi"}],"date_created":"2024-04-07T12:53:32Z","title":"Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems","doi":"10.1016/j.jde.2023.07.029","publication_identifier":{"issn":["0022-0396"]},"publication_status":"published","year":"2023","intvolume":" 374","page":"1-28","citation":{"apa":"Winkler, M., & Yokota, T. (2023). Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems. Journal of Differential Equations, 374, 1–28. https://doi.org/10.1016/j.jde.2023.07.029","mla":"Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena by Arbitrarily Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes Systems.” Journal of Differential Equations, vol. 374, Elsevier BV, 2023, pp. 1–28, doi:10.1016/j.jde.2023.07.029.","short":"M. Winkler, T. Yokota, Journal of Differential Equations 374 (2023) 1–28.","bibtex":"@article{Winkler_Yokota_2023, title={Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems}, volume={374}, DOI={10.1016/j.jde.2023.07.029}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler, Michael and Yokota, Tomomi}, year={2023}, pages={1–28} }","ieee":"M. Winkler and T. Yokota, “Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems,” Journal of Differential Equations, vol. 374, pp. 1–28, 2023, doi: 10.1016/j.jde.2023.07.029.","chicago":"Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena by Arbitrarily Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes Systems.” Journal of Differential Equations 374 (2023): 1–28. https://doi.org/10.1016/j.jde.2023.07.029.","ama":"Winkler M, Yokota T. Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems. Journal of Differential Equations. 2023;374:1-28. doi:10.1016/j.jde.2023.07.029"},"_id":"53342","user_id":"31496","keyword":["Analysis","Applied Mathematics"],"language":[{"iso":"eng"}],"publication":"Journal of Differential Equations","type":"journal_article","status":"public"},{"status":"public","type":"journal_article","publication":"Advances in Differential Equations","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Analysis"],"user_id":"31496","_id":"53346","citation":{"ieee":"M. Winkler, “Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing,” Advances in Differential Equations, vol. 28, no. 11/12, 2023, doi: 10.57262/ade028-1112-921.","chicago":"Winkler, Michael. “Absence of Collapse into Persistent Dirac-Type Singularities in a Keller-Segel-Navier-Stokes System Involving Local Sensing.” Advances in Differential Equations 28, no. 11/12 (2023). https://doi.org/10.57262/ade028-1112-921.","ama":"Winkler M. Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing. Advances in Differential Equations. 2023;28(11/12). doi:10.57262/ade028-1112-921","apa":"Winkler, M. (2023). Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing. Advances in Differential Equations, 28(11/12). https://doi.org/10.57262/ade028-1112-921","mla":"Winkler, Michael. “Absence of Collapse into Persistent Dirac-Type Singularities in a Keller-Segel-Navier-Stokes System Involving Local Sensing.” Advances in Differential Equations, vol. 28, no. 11/12, Khayyam Publishing, Inc, 2023, doi:10.57262/ade028-1112-921.","short":"M. Winkler, Advances in Differential Equations 28 (2023).","bibtex":"@article{Winkler_2023, title={Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing}, volume={28}, DOI={10.57262/ade028-1112-921}, number={11/12}, journal={Advances in Differential Equations}, publisher={Khayyam Publishing, Inc}, author={Winkler, Michael}, year={2023} }"},"intvolume":" 28","year":"2023","issue":"11/12","publication_status":"published","publication_identifier":{"issn":["1079-9389"]},"doi":"10.57262/ade028-1112-921","title":"Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing","author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2024-04-07T12:57:19Z","volume":28,"date_updated":"2024-04-07T12:57:23Z","publisher":"Khayyam Publishing, Inc"},{"_id":"45984","user_id":"15458","language":[{"iso":"eng"}],"type":"journal_article","publication":"Proc. ACM Hum. Comput. Interact.","status":"public","date_updated":"2024-04-09T07:19:23Z","date_created":"2023-07-11T06:23:54Z","author":[{"last_name":"Kaur","full_name":"Kaur, Mannat","first_name":"Mannat"},{"id":"99000","full_name":"Sri Ramulu, Harshini","orcid":"0000-0002-0000-5843","last_name":"Sri Ramulu","first_name":"Harshini"},{"last_name":"Acar","full_name":"Acar, Yasemin","first_name":"Yasemin"},{"full_name":"Fiebig, Tobias","last_name":"Fiebig","first_name":"Tobias"}],"volume":7,"title":"\"Oh yes! over-preparing for meetings is my jam :)\": The Gendered Experiences of System Administrators","doi":"10.1145/3579617","issue":"CSCW1","year":"2023","citation":{"mla":"Kaur, Mannat, et al. “‘Oh Yes! Over-Preparing for Meetings Is My Jam :)’: The Gendered Experiences of System Administrators.” Proc. ACM Hum. Comput. Interact., vol. 7, no. CSCW1, 2023, pp. 1–38, doi:10.1145/3579617.","bibtex":"@article{Kaur_Sri Ramulu_Acar_Fiebig_2023, title={“Oh yes! over-preparing for meetings is my jam :)”: The Gendered Experiences of System Administrators}, volume={7}, DOI={10.1145/3579617}, number={CSCW1}, journal={Proc. ACM Hum. Comput. Interact.}, author={Kaur, Mannat and Sri Ramulu, Harshini and Acar, Yasemin and Fiebig, Tobias}, year={2023}, pages={1–38} }","short":"M. Kaur, H. Sri Ramulu, Y. Acar, T. Fiebig, Proc. ACM Hum. Comput. Interact. 7 (2023) 1–38.","apa":"Kaur, M., Sri Ramulu, H., Acar, Y., & Fiebig, T. (2023). “Oh yes! over-preparing for meetings is my jam :)”: The Gendered Experiences of System Administrators. Proc. ACM Hum. Comput. Interact., 7(CSCW1), 1–38. https://doi.org/10.1145/3579617","ieee":"M. Kaur, H. Sri Ramulu, Y. Acar, and T. Fiebig, “‘Oh yes! over-preparing for meetings is my jam :)’: The Gendered Experiences of System Administrators,” Proc. ACM Hum. Comput. Interact., vol. 7, no. CSCW1, pp. 1–38, 2023, doi: 10.1145/3579617.","chicago":"Kaur, Mannat, Harshini Sri Ramulu, Yasemin Acar, and Tobias Fiebig. “‘Oh Yes! Over-Preparing for Meetings Is My Jam :)’: The Gendered Experiences of System Administrators.” Proc. ACM Hum. Comput. Interact. 7, no. CSCW1 (2023): 1–38. https://doi.org/10.1145/3579617.","ama":"Kaur M, Sri Ramulu H, Acar Y, Fiebig T. “Oh yes! over-preparing for meetings is my jam :)”: The Gendered Experiences of System Administrators. Proc ACM Hum Comput Interact. 2023;7(CSCW1):1–38. doi:10.1145/3579617"},"page":"1–38","intvolume":" 7"},{"place":"Wiesbaden","year":"2023","citation":{"ama":"Werth G. Neue Wege Im Mathematischen Unterricht: Auf Den Spuren Mathilde Vaertings. Springer Fachmedien Wiesbaden; 2023. doi:10.1007/978-3-658-42445-9","ieee":"G. Werth, Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings. Wiesbaden: Springer Fachmedien Wiesbaden, 2023.","chicago":"Werth, Gerda. Neue Wege Im Mathematischen Unterricht: Auf Den Spuren Mathilde Vaertings. Wiesbaden: Springer Fachmedien Wiesbaden, 2023. https://doi.org/10.1007/978-3-658-42445-9.","mla":"Werth, Gerda. Neue Wege Im Mathematischen Unterricht: Auf Den Spuren Mathilde Vaertings. Springer Fachmedien Wiesbaden, 2023, doi:10.1007/978-3-658-42445-9.","short":"G. Werth, Neue Wege Im Mathematischen Unterricht: Auf Den Spuren Mathilde Vaertings, Springer Fachmedien Wiesbaden, Wiesbaden, 2023.","bibtex":"@book{Werth_2023, place={Wiesbaden}, title={Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings}, DOI={10.1007/978-3-658-42445-9}, publisher={Springer Fachmedien Wiesbaden}, author={Werth, Gerda}, year={2023} }","apa":"Werth, G. (2023). Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings. Springer Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-42445-9"},"publication_identifier":{"isbn":["9783658424442","9783658424459"],"issn":["2661-8591","2661-8605"]},"publication_status":"published","title":"Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings","doi":"10.1007/978-3-658-42445-9","publisher":"Springer Fachmedien Wiesbaden","date_updated":"2024-04-09T11:07:16Z","author":[{"first_name":"Gerda","last_name":"Werth","id":"578","full_name":"Werth, Gerda"}],"date_created":"2024-01-31T13:08:37Z","status":"public","type":"book","language":[{"iso":"eng"}],"_id":"51101","department":[{"_id":"34"},{"_id":"10"},{"_id":"98"},{"_id":"360"}],"user_id":"578"},{"status":"public","type":"journal_article","publication":"mathematik lehren","language":[{"iso":"ger"}],"_id":"51103","user_id":"578","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"360"}],"year":"2023","citation":{"ama":"Werth G. Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe. mathematik lehren. 2023;241:15-19.","chicago":"Werth, Gerda. “Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe.” mathematik lehren 241 (2023): 15–19.","ieee":"G. Werth, “Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe,” mathematik lehren, vol. 241, pp. 15–19, 2023.","bibtex":"@article{Werth_2023, title={Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe}, volume={241}, journal={mathematik lehren}, publisher={Friedrich}, author={Werth, Gerda}, year={2023}, pages={15–19} }","short":"G. Werth, mathematik lehren 241 (2023) 15–19.","mla":"Werth, Gerda. “Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe.” mathematik lehren, vol. 241, Friedrich, 2023, pp. 15–19.","apa":"Werth, G. (2023). Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe. mathematik lehren, 241, 15–19."},"intvolume":" 241","page":"15-19","publication_status":"published","title":"Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe","date_updated":"2024-04-09T09:19:05Z","publisher":"Friedrich","date_created":"2024-01-31T13:15:50Z","author":[{"last_name":"Werth","id":"578","full_name":"Werth, Gerda","first_name":"Gerda"}],"volume":241},{"type":"conference","status":"public","project":[{"grant_number":"418701707","name":"TRR 285: TRR 285","_id":"130"},{"name":"TRR 285 - B: TRR 285 - Project Area B","_id":"132"},{"_id":"143","name":"TRR 285 – B04: TRR 285 - Subproject B04"}],"_id":"51739","user_id":"45673","department":[{"_id":"143"},{"_id":"630"}],"language":[{"iso":"ger"}],"publication_status":"published","year":"2023","citation":{"ama":"Weiß D, Duffe T, Buczek M, Kullmer G, Schramm B. Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss. In: Deutscher Verband für Materialforschung und -prüfung e.V.; 2023. doi:10.48447/WP-2023-244","chicago":"Weiß, Deborah, Tobias Duffe, Moritz Buczek, Gunter Kullmer, and Britta Schramm. “Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss.” Deutscher Verband für Materialforschung und -prüfung e.V., 2023. https://doi.org/10.48447/WP-2023-244.","ieee":"D. Weiß, T. Duffe, M. Buczek, G. Kullmer, and B. Schramm, “Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss,” presented at the Werkstoffprüfung 2023: Werkstoffe und Bauteile auf dem Prüfstand - Tagung, Berlin, 2023, doi: 10.48447/WP-2023-244.","apa":"Weiß, D., Duffe, T., Buczek, M., Kullmer, G., & Schramm, B. (2023). Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss. Werkstoffprüfung 2023: Werkstoffe und Bauteile auf dem Prüfstand - Tagung, Berlin. https://doi.org/10.48447/WP-2023-244","mla":"Weiß, Deborah, et al. Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss. Deutscher Verband für Materialforschung und -prüfung e.V., 2023, doi:10.48447/WP-2023-244.","short":"D. Weiß, T. Duffe, M. Buczek, G. Kullmer, B. Schramm, in: Deutscher Verband für Materialforschung und -prüfung e.V., 2023.","bibtex":"@inproceedings{Weiß_Duffe_Buczek_Kullmer_Schramm_2023, title={Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss}, DOI={10.48447/WP-2023-244}, publisher={Deutscher Verband für Materialforschung und -prüfung e.V.}, author={Weiß, Deborah and Duffe, Tobias and Buczek, Moritz and Kullmer, Gunter and Schramm, Britta}, year={2023} }"},"publisher":"Deutscher Verband für Materialforschung und -prüfung e.V.","date_updated":"2024-04-10T07:08:49Z","author":[{"first_name":"Deborah","id":"45673","full_name":"Weiß, Deborah","last_name":"Weiß"},{"first_name":"Tobias","last_name":"Duffe","full_name":"Duffe, Tobias","id":"41322"},{"first_name":"Moritz","id":"83727","full_name":"Buczek, Moritz","last_name":"Buczek"},{"last_name":"Kullmer","id":"291","full_name":"Kullmer, Gunter","first_name":"Gunter"},{"first_name":"Britta","last_name":"Schramm","full_name":"Schramm, Britta","id":"4668"}],"date_created":"2024-02-22T09:54:40Z","title":"Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss","doi":"10.48447/WP-2023-244","conference":{"location":"Berlin","end_date":"2023-11-24","start_date":"2023-11-23","name":"Werkstoffprüfung 2023: Werkstoffe und Bauteile auf dem Prüfstand - Tagung"}},{"doi":"https://doi.org/10.1515/9783110745504","title":"CLIL - Content and Language Integrated Learning","date_created":"2023-01-10T23:28:10Z","author":[{"id":"65153","full_name":"Böttger, Lydia","last_name":"Böttger","first_name":"Lydia"},{"last_name":"Niederhaus","id":"54999","full_name":"Niederhaus, Constanze","first_name":"Constanze"}],"publisher":"De Gruyter","date_updated":"2024-04-10T14:59:38Z","citation":{"mla":"Böttger, Lydia, and Constanze Niederhaus. “CLIL - Content and Language Integrated Learning.” Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive, edited by Christian Efing and Zeynep Kalkavan-Aydin, De Gruyter, 2023, doi:https://doi.org/10.1515/9783110745504.","bibtex":"@inbook{Böttger_Niederhaus_2023, place={Berlin/Boston}, title={CLIL - Content and Language Integrated Learning}, DOI={https://doi.org/10.1515/9783110745504}, booktitle={Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive}, publisher={De Gruyter}, author={Böttger, Lydia and Niederhaus, Constanze}, editor={Efing, Christian and Kalkavan-Aydin, Zeynep}, year={2023} }","short":"L. Böttger, C. Niederhaus, in: C. Efing, Z. Kalkavan-Aydin (Eds.), Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive, De Gruyter, Berlin/Boston, 2023.","apa":"Böttger, L., & Niederhaus, C. (2023). CLIL - Content and Language Integrated Learning. In C. Efing & Z. Kalkavan-Aydin (Eds.), Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive. De Gruyter. https://doi.org/10.1515/9783110745504","ama":"Böttger L, Niederhaus C. CLIL - Content and Language Integrated Learning. In: Efing C, Kalkavan-Aydin Z, eds. Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive. De Gruyter; 2023. doi:https://doi.org/10.1515/9783110745504","chicago":"Böttger, Lydia, and Constanze Niederhaus. “CLIL - Content and Language Integrated Learning.” In Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive, edited by Christian Efing and Zeynep Kalkavan-Aydin. Berlin/Boston: De Gruyter, 2023. https://doi.org/10.1515/9783110745504.","ieee":"L. Böttger and C. Niederhaus, “CLIL - Content and Language Integrated Learning,” in Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive, C. Efing and Z. Kalkavan-Aydin, Eds. Berlin/Boston: De Gruyter, 2023."},"year":"2023","place":"Berlin/Boston","publication_status":"published","language":[{"iso":"ger"}],"user_id":"65153","department":[{"_id":"5"}],"_id":"35904","status":"public","editor":[{"last_name":"Efing","full_name":"Efing, Christian","first_name":"Christian"},{"first_name":"Zeynep","last_name":"Kalkavan-Aydin","full_name":"Kalkavan-Aydin, Zeynep"}],"type":"book_chapter","publication":"Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive"},{"citation":{"mla":"Wolf, Lasse L., and Hong-Wei Zhang. “$L^2$-Spectrum, Growth Indicator Function and Critical Exponent on  Locally Symmetric Spaces.” ArXiv:2311.11770, 2023.","bibtex":"@article{Wolf_Zhang_2023, title={$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces}, journal={arXiv:2311.11770}, author={Wolf, Lasse L. and Zhang, Hong-Wei}, year={2023} }","short":"L.L. Wolf, H.-W. Zhang, ArXiv:2311.11770 (2023).","apa":"Wolf, L. L., & Zhang, H.-W. (2023). $L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces. In arXiv:2311.11770.","ieee":"L. L. Wolf and H.-W. Zhang, “$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces,” arXiv:2311.11770. 2023.","chicago":"Wolf, Lasse L., and Hong-Wei Zhang. “$L^2$-Spectrum, Growth Indicator Function and Critical Exponent on  Locally Symmetric Spaces.” ArXiv:2311.11770, 2023.","ama":"Wolf LL, Zhang H-W. $L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces. arXiv:231111770. Published online 2023."},"year":"2023","title":"$L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces","author":[{"first_name":"Lasse L.","last_name":"Wolf","full_name":"Wolf, Lasse L."},{"first_name":"Hong-Wei","full_name":"Zhang, Hong-Wei","last_name":"Zhang"}],"date_created":"2024-04-10T13:45:59Z","date_updated":"2024-04-10T13:48:17Z","status":"public","abstract":[{"lang":"eng","text":"In this short note we observe, on locally symmetric spaces of higher rank, a\r\nconnection between the growth indicator function introduced by Quint and the\r\nmodified critical exponent of the Poincar\\'e series equipped with the\r\npolyhedral distance. As a consequence, we provide a different characterization\r\nof the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms\r\nof the growth indicator function. Moreover, we explore the relationship between\r\nthese three objects and the temperedness."}],"publication":"arXiv:2311.11770","type":"preprint","language":[{"iso":"eng"}],"department":[{"_id":"10"},{"_id":"548"}],"user_id":"45027","_id":"53404","external_id":{"arxiv":["2311.11770"]}},{"citation":{"ieee":"T. Jenert, “Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis,” in Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung, H.-H. Kremer, H. Ertl, and P. F. E. Sloane, Eds. Bonn: Bundesinstitut für Berufsbildung., 2023, pp. 11–24.","chicago":"Jenert, Tobias. “Design-Based Research Als Erforschung Und Gestaltung von Interaktionsprozessen Zwischen Wissenschaft Und Bildungspraxis.” In Wissenschaft Trifft Praxis – Designbasierte Forschung in Der Beruflichen Bildung, edited by H.-Hugo Kremer, Hubert Ertl, and Peter F. E. Sloane, 11–24. Bonn: Bundesinstitut für Berufsbildung., 2023.","ama":"Jenert T. Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis. In: Kremer H-H, Ertl H, Sloane PFE, eds. Wissenschaft Trifft Praxis – Designbasierte Forschung in Der Beruflichen Bildung. Bundesinstitut für Berufsbildung.; 2023:11-24.","apa":"Jenert, T. (2023). Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis. In H.-H. Kremer, H. Ertl, & P. F. E. Sloane (Eds.), Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung (pp. 11–24). Bundesinstitut für Berufsbildung.","bibtex":"@inbook{Jenert_2023, place={Bonn}, title={Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis}, booktitle={Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung}, publisher={Bundesinstitut für Berufsbildung.}, author={Jenert, Tobias}, editor={Kremer, H.-Hugo and Ertl, Hubert and Sloane, Peter F. E.}, year={2023}, pages={11–24} }","mla":"Jenert, Tobias. “Design-Based Research Als Erforschung Und Gestaltung von Interaktionsprozessen Zwischen Wissenschaft Und Bildungspraxis.” Wissenschaft Trifft Praxis – Designbasierte Forschung in Der Beruflichen Bildung, edited by H.-Hugo Kremer et al., Bundesinstitut für Berufsbildung., 2023, pp. 11–24.","short":"T. Jenert, in: H.-H. Kremer, H. Ertl, P.F.E. Sloane (Eds.), Wissenschaft Trifft Praxis – Designbasierte Forschung in Der Beruflichen Bildung, Bundesinstitut für Berufsbildung., Bonn, 2023, pp. 11–24."},"page":"11-24","year":"2023","place":"Bonn","quality_controlled":"1","main_file_link":[{"url":"https://www.bibb.de/dienst/publikationen/de/download/18616"}],"title":"Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis","date_created":"2024-04-11T06:29:37Z","author":[{"first_name":"Tobias","id":"71994","full_name":"Jenert, Tobias","orcid":" https://orcid.org/0000-0001-9262-5646","last_name":"Jenert"}],"date_updated":"2024-04-11T06:30:05Z","publisher":"Bundesinstitut für Berufsbildung.","status":"public","abstract":[{"text":"Das Verhältnis zwischen Wissenschaft und Praxis wurde in unterschiedlichen Forschungsansätzen im-\r\nmer wieder wissenschaftlich betrachtet. Dennoch ist es notwendig, sich im Rahmen der wissenschafts-\r\ntheoretischen Konzeption von Design-Based Research (DBR) weiter damit auseinanderzusetzen, denn\r\nInteraktion zwischen Wissenschaft und Bildungspraxis ist ein zentrales Merkmal von DBR. Dieser Beitrag\r\nbefasst sich mit der Frage, wie sich diese Interaktion je nach zugrunde liegendem DBR-Verständnis me-\r\nthodologisch fassen lässt. Die Interaktion wird als ein wesentlicher Bestandteil des Erkenntnisprozesses\r\nin DBR aufgefasst. Daher wird neben der methodischen Ausgestaltung von Interaktionsprozessen auch\r\nmethodologisch reflektiert, was die Wissenschaft-Praxis-Interaktion für die Erkenntnis an sich bedeutet.","lang":"eng"}],"editor":[{"first_name":"H.-Hugo","full_name":"Kremer, H.-Hugo","last_name":"Kremer"},{"last_name":"Ertl","full_name":"Ertl, Hubert","first_name":"Hubert"},{"last_name":"Sloane","full_name":"Sloane, Peter F. E.","first_name":"Peter F. E."}],"type":"book_chapter","publication":"Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung","language":[{"iso":"eng"}],"user_id":"71994","department":[{"_id":"208"}],"_id":"53405"},{"user_id":"58465","department":[{"_id":"67"}],"_id":"52380","language":[{"iso":"eng"}],"type":"conference","publication":"Proceedings of the 23rd Koli Calling International Conference on Computing Education Research","status":"public","date_created":"2024-03-08T08:02:10Z","author":[{"id":"63216","full_name":"Sparmann, Sören","last_name":"Sparmann","first_name":"Sören"},{"full_name":"Hüsing, Sven","id":"58465","last_name":"Hüsing","first_name":"Sven"},{"first_name":"Carsten","full_name":"Schulte, Carsten","id":"60311","last_name":"Schulte"}],"publisher":"ACM","date_updated":"2024-04-11T12:30:59Z","doi":"10.1145/3631802.3631824","title":"JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks","publication_status":"published","citation":{"apa":"Sparmann, S., Hüsing, S., & Schulte, C. (2023). JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks. Proceedings of the 23rd Koli Calling International Conference on Computing Education Research. https://doi.org/10.1145/3631802.3631824","short":"S. Sparmann, S. Hüsing, C. Schulte, in: Proceedings of the 23rd Koli Calling International Conference on Computing Education Research, ACM, 2023.","bibtex":"@inproceedings{Sparmann_Hüsing_Schulte_2023, title={JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks}, DOI={10.1145/3631802.3631824}, booktitle={Proceedings of the 23rd Koli Calling International Conference on Computing Education Research}, publisher={ACM}, author={Sparmann, Sören and Hüsing, Sven and Schulte, Carsten}, year={2023} }","mla":"Sparmann, Sören, et al. “JuGaze: A Cell-Based Eye Tracking and Logging Tool for Jupyter Notebooks.” Proceedings of the 23rd Koli Calling International Conference on Computing Education Research, ACM, 2023, doi:10.1145/3631802.3631824.","ama":"Sparmann S, Hüsing S, Schulte C. JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks. In: Proceedings of the 23rd Koli Calling International Conference on Computing Education Research. ACM; 2023. doi:10.1145/3631802.3631824","ieee":"S. Sparmann, S. Hüsing, and C. Schulte, “JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks,” 2023, doi: 10.1145/3631802.3631824.","chicago":"Sparmann, Sören, Sven Hüsing, and Carsten Schulte. “JuGaze: A Cell-Based Eye Tracking and Logging Tool for Jupyter Notebooks.” In Proceedings of the 23rd Koli Calling International Conference on Computing Education Research. ACM, 2023. https://doi.org/10.1145/3631802.3631824."},"year":"2023"},{"department":[{"_id":"548"}],"user_id":"70575","_id":"53410","language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"publication":"Annales Henri Poincaré","type":"journal_article","status":"public","abstract":[{"text":"AbstractWe consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing, the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016) can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.","lang":"eng"}],"volume":25,"author":[{"first_name":"Benjamin","last_name":"Delarue","id":"70575","full_name":"Delarue, Benjamin"},{"first_name":"Philipp","last_name":"Schütte","id":"50168","full_name":"Schütte, Philipp"},{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919"}],"date_created":"2024-04-11T12:30:14Z","publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-11T12:37:34Z","doi":"10.1007/s00023-023-01379-x","title":"Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models","issue":"2","publication_identifier":{"issn":["1424-0637","1424-0661"]},"publication_status":"published","page":"1607-1656","intvolume":" 25","citation":{"apa":"Delarue, B., Schütte, P., & Weich, T. (2023). Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. Annales Henri Poincaré, 25(2), 1607–1656. https://doi.org/10.1007/s00023-023-01379-x","mla":"Delarue, Benjamin, et al. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” Annales Henri Poincaré, vol. 25, no. 2, Springer Science and Business Media LLC, 2023, pp. 1607–56, doi:10.1007/s00023-023-01379-x.","short":"B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.","bibtex":"@article{Delarue_Schütte_Weich_2023, title={Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}, volume={25}, DOI={10.1007/s00023-023-01379-x}, number={2}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}, year={2023}, pages={1607–1656} }","ieee":"B. Delarue, P. Schütte, and T. Weich, “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” Annales Henri Poincaré, vol. 25, no. 2, pp. 1607–1656, 2023, doi: 10.1007/s00023-023-01379-x.","chicago":"Delarue, Benjamin, Philipp Schütte, and Tobias Weich. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” Annales Henri Poincaré 25, no. 2 (2023): 1607–56. https://doi.org/10.1007/s00023-023-01379-x.","ama":"Delarue B, Schütte P, Weich T. Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. Annales Henri Poincaré. 2023;25(2):1607-1656. doi:10.1007/s00023-023-01379-x"},"year":"2023"}]