--- _id: '63256' article_number: '113600' author: - first_name: Vanja full_name: Nikolić, Vanja last_name: Nikolić - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: ama: Nikolić V, Winkler M. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si15.svg" display="inline" id="d1e25"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation. Nonlinear Analysis. 2024;247. doi:10.1016/j.na.2024.113600 apa: Nikolić, V., & Winkler, M. (2024). <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si15.svg" display="inline" id="d1e25"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation. Nonlinear Analysis, 247, Article 113600. https://doi.org/10.1016/j.na.2024.113600 bibtex: '@article{Nikolić_Winkler_2024, title={<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si15.svg" display="inline" id="d1e25"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation}, volume={247}, DOI={10.1016/j.na.2024.113600}, number={113600}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Nikolić, Vanja and Winkler, Michael}, year={2024} }' chicago: Nikolić, Vanja, and Michael Winkler. “<mml:Math Xmlns:Mml="http://Www.W3.Org/1998/Math/MathML" Altimg="si15.Svg" Display="inline" Id="d1e25"><mml:Msup><mml:Mrow><mml:Mi>L</Mml:Mi></Mml:Mrow><mml:Mrow><mml:Mi>∞</Mml:Mi></Mml:Mrow></Mml:Msup></Mml:Math> Blow-up in the Jordan–Moore–Gibson–Thompson Equation.” Nonlinear Analysis 247 (2024). https://doi.org/10.1016/j.na.2024.113600. ieee: 'V. Nikolić and M. Winkler, “<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si15.svg" display="inline" id="d1e25"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation,” Nonlinear Analysis, vol. 247, Art. no. 113600, 2024, doi: 10.1016/j.na.2024.113600.' mla: Nikolić, Vanja, and Michael Winkler. “<mml:Math Xmlns:Mml="http://Www.W3.Org/1998/Math/MathML" Altimg="si15.Svg" Display="inline" Id="d1e25"><mml:Msup><mml:Mrow><mml:Mi>L</Mml:Mi></Mml:Mrow><mml:Mrow><mml:Mi>∞</Mml:Mi></Mml:Mrow></Mml:Msup></Mml:Math> Blow-up in the Jordan–Moore–Gibson–Thompson Equation.” Nonlinear Analysis, vol. 247, 113600, Elsevier BV, 2024, doi:10.1016/j.na.2024.113600. short: V. Nikolić, M. Winkler, Nonlinear Analysis 247 (2024). date_created: 2025-12-18T19:06:09Z date_updated: 2025-12-18T20:14:12Z doi: 10.1016/j.na.2024.113600 intvolume: ' 247' language: - iso: eng publication: Nonlinear Analysis publication_identifier: issn: - 0362-546X publication_status: published publisher: Elsevier BV status: public title: L∞ blow-up in the Jordan–Moore–Gibson–Thompson equation type: journal_article user_id: '31496' volume: 247 year: '2024' ... --- _id: '63260' abstract: - lang: eng text: "AbstractA no‐flux initial‐boundary value problem for\r\nis considered in a ball , where and .Under the assumption that , it is shown that for each , there exist and a positive \ with the property that whenever is nonnegative with , the global solutions to () emanating from the initial data have the property that\r\n" author: - first_name: Yulan full_name: Wang, Yulan last_name: Wang - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: ama: Wang Y, Winkler M. A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities. Mathematische Nachrichten. 2024;297(6):2353-2364. doi:10.1002/mana.202300361 apa: Wang, Y., & Winkler, M. (2024). A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities. Mathematische Nachrichten, 297(6), 2353–2364. https://doi.org/10.1002/mana.202300361 bibtex: '@article{Wang_Winkler_2024, title={A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities}, volume={297}, DOI={10.1002/mana.202300361}, number={6}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024}, pages={2353–2364} }' chicago: 'Wang, Yulan, and Michael Winkler. “A Singular Growth Phenomenon in a Keller–Segel–Type Parabolic System Involving Density‐suppressed Motilities.” Mathematische Nachrichten 297, no. 6 (2024): 2353–64. https://doi.org/10.1002/mana.202300361.' ieee: 'Y. Wang and M. Winkler, “A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities,” Mathematische Nachrichten, vol. 297, no. 6, pp. 2353–2364, 2024, doi: 10.1002/mana.202300361.' mla: Wang, Yulan, and Michael Winkler. “A Singular Growth Phenomenon in a Keller–Segel–Type Parabolic System Involving Density‐suppressed Motilities.” Mathematische Nachrichten, vol. 297, no. 6, Wiley, 2024, pp. 2353–64, doi:10.1002/mana.202300361. short: Y. Wang, M. Winkler, Mathematische Nachrichten 297 (2024) 2353–2364. date_created: 2025-12-18T19:07:48Z date_updated: 2025-12-18T20:14:46Z doi: 10.1002/mana.202300361 intvolume: ' 297' issue: '6' language: - iso: eng page: 2353-2364 publication: Mathematische Nachrichten publication_identifier: issn: - 0025-584X - 1522-2616 publication_status: published publisher: Wiley status: public title: A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities type: journal_article user_id: '31496' volume: 297 year: '2024' ... --- _id: '63262' abstract: - lang: eng text: "AbstractRadially symmetric global unbounded solutions of the chemotaxis system

$$\\left\\{ {\\matrix{{{u_t} = \\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (uS(u)\\nabla v),} \\hfill & {} \\hfill \\cr {0 = \\Delta v - \\mu + u,} \\hfill & {\\mu = {1 \\over {|\\Omega |}}\\int_\\Omega {u,} } \\hfill \\cr } } \\right.$$

\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 ∇\r\n \ ⋅\r\n (\r\n \ D\r\n (\r\n \ u\r\n )\r\n \ ∇\r\n u\r\n \ )\r\n −\r\n \ ∇\r\n ⋅\r\n \ (\r\n u\r\n \ S\r\n (\r\n \ u\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 \ \r\n \r\n \ \r\n 0\r\n \ =\r\n Δ\r\n \ v\r\n −\r\n \ μ\r\n +\r\n \ u\r\n ,\r\n \ \r\n \r\n \ \r\n \r\n \ μ\r\n =\r\n \ \r\n 1\r\n \ \r\n |\r\n \ Ω\r\n |\r\n \ \r\n \r\n \ \r\n \r\n \ \r\n ∫\r\n \ Ω\r\n \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 \ are considered in a ball Ω = BR(0) ⊂ ℝn, where n ≥ 3 and R > 0.Under the assumption that D and S suitably generalize the prototypes given by D(ξ) = (ξ + ι)m−1 and S(ξ) = (ξ + 1)−λ−1 for all ξ > 0 and some m ∈ ℝ, λ >0 and ι ≥ 0 fulfilling

$$m + \\lambda < 1 - {2 \\over n}$$

\r\n \ m\r\n +\r\n \ λ\r\n <\r\n \ 1\r\n −\r\n \ \r\n 2\r\n n\r\n \ \r\n , a considerably large set of initial data u0 is found to enforce a complete mass aggregation in infinite time in the sense that for any such u0, an associated Neumann type initial-boundary value problem admits a global classical solution (u, v) satisfying

$${1 \\over C} \\cdot {(t + 1)^{{1 \\over \\lambda }}} \\le ||u( \\cdot ,t)|{|_{{L^\\infty }(\\Omega )}} \\le C \\cdot {(t + 1)^{{1 \\over \\lambda }}}\\,\\,\\,{\\rm{for}}\\,\\,{\\rm{all}}\\,\\,t > 0$$

\r\n \ \r\n \r\n 1\r\n \ C\r\n \r\n \ \r\n ⋅\r\n \r\n \ (\r\n t\r\n \ +\r\n 1\r\n \ \r\n )\r\n \ \r\n \r\n \r\n \ 1\r\n λ\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 ,\r\n \ t\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 \ L\r\n ∞\r\n \ \r\n \r\n \ (\r\n Ω\r\n \ )\r\n \r\n \ \r\n \r\n ≤\r\n \ C\r\n ⋅\r\n \ \r\n (\r\n t\r\n \ +\r\n 1\r\n \ \r\n )\r\n \ \r\n \r\n \r\n \ 1\r\n λ\r\n \ \r\n \r\n \ \r\n \r\n \r\n \ \r\n \r\n \r\n \ \r\n \r\n f\r\n \ o\r\n r\r\n \ \r\n \r\n \r\n \ \r\n \r\n \r\n \ a\r\n l\r\n \ l\r\n \r\n \ \r\n \r\n \r\n \ t\r\n >\r\n \ 0\r\n as well as

$$||u( \\cdot \\,,t)|{|_{{L^1}(\\Omega \\backslash {B_{{r_0}}}(0))}} \\to 0\\,\\,\\,{\\rm{as}}\\,\\,t \\to \\infty \\,\\,\\,{\\rm{for}}\\,\\,{\\rm{all}}\\,\\,{r_0} \\in (0,R)$$

\r\n |\r\n \ |\r\n u\r\n \ (\r\n ⋅\r\n \ ,\r\n t\r\n \ )\r\n |\r\n \ \r\n |\r\n \r\n \ \r\n L\r\n \ 1\r\n \r\n \ (\r\n Ω\r\n \ \\\r\n \r\n \ B\r\n \r\n \ \r\n r\r\n \ 0\r\n \r\n \ \r\n \r\n (\r\n \ 0\r\n )\r\n \ )\r\n \r\n \ \r\n →\r\n 0\r\n \ as\r\n t\r\n \ →\r\n ∞\r\n \ for all\r\n \r\n \ r\r\n 0\r\n \ \r\n ∈\r\n (\r\n \ 0\r\n ,\r\n \ R\r\n )\r\n \ with some C > 0." author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: ama: Winkler M. Complete infinite-time mass aggregation in a quasilinear Keller–Segel system. Israel Journal of Mathematics. 2024;263(1):93-127. doi:10.1007/s11856-024-2618-9 apa: Winkler, M. (2024). Complete infinite-time mass aggregation in a quasilinear Keller–Segel system. Israel Journal of Mathematics, 263(1), 93–127. https://doi.org/10.1007/s11856-024-2618-9 bibtex: '@article{Winkler_2024, title={Complete infinite-time mass aggregation in a quasilinear Keller–Segel system}, volume={263}, DOI={10.1007/s11856-024-2618-9}, number={1}, journal={Israel Journal of Mathematics}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2024}, pages={93–127} }' chicago: 'Winkler, Michael. “Complete Infinite-Time Mass Aggregation in a Quasilinear Keller–Segel System.” Israel Journal of Mathematics 263, no. 1 (2024): 93–127. https://doi.org/10.1007/s11856-024-2618-9.' ieee: 'M. Winkler, “Complete infinite-time mass aggregation in a quasilinear Keller–Segel system,” Israel Journal of Mathematics, vol. 263, no. 1, pp. 93–127, 2024, doi: 10.1007/s11856-024-2618-9.' mla: Winkler, Michael. “Complete Infinite-Time Mass Aggregation in a Quasilinear Keller–Segel System.” Israel Journal of Mathematics, vol. 263, no. 1, Springer Science and Business Media LLC, 2024, pp. 93–127, doi:10.1007/s11856-024-2618-9. short: M. Winkler, Israel Journal of Mathematics 263 (2024) 93–127. date_created: 2025-12-18T19:08:34Z date_updated: 2025-12-18T20:14:59Z doi: 10.1007/s11856-024-2618-9 intvolume: ' 263' issue: '1' language: - iso: eng page: 93-127 publication: Israel Journal of Mathematics publication_identifier: issn: - 0021-2172 - 1565-8511 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Complete infinite-time mass aggregation in a quasilinear Keller–Segel system type: journal_article user_id: '31496' volume: 263 year: '2024' ... --- _id: '63263' author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: ama: Winkler M. L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux. Journal of Differential Equations. 2024;400:423-456. doi:10.1016/j.jde.2024.04.028 apa: Winkler, M. (2024). L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux. Journal of Differential Equations, 400, 423–456. https://doi.org/10.1016/j.jde.2024.04.028 bibtex: '@article{Winkler_2024, title={L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux}, volume={400}, DOI={10.1016/j.jde.2024.04.028}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler, Michael}, year={2024}, pages={423–456} }' chicago: 'Winkler, Michael. “L∞ Bounds in a Two-Dimensional Doubly Degenerate Nutrient Taxis System with General Cross-Diffusive Flux.” Journal of Differential Equations 400 (2024): 423–56. https://doi.org/10.1016/j.jde.2024.04.028.' ieee: 'M. Winkler, “L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux,” Journal of Differential Equations, vol. 400, pp. 423–456, 2024, doi: 10.1016/j.jde.2024.04.028.' mla: Winkler, Michael. “L∞ Bounds in a Two-Dimensional Doubly Degenerate Nutrient Taxis System with General Cross-Diffusive Flux.” Journal of Differential Equations, vol. 400, Elsevier BV, 2024, pp. 423–56, doi:10.1016/j.jde.2024.04.028. short: M. Winkler, Journal of Differential Equations 400 (2024) 423–456. date_created: 2025-12-18T19:09:07Z date_updated: 2025-12-18T20:15:05Z doi: 10.1016/j.jde.2024.04.028 intvolume: ' 400' language: - iso: eng page: 423-456 publication: Journal of Differential Equations publication_identifier: issn: - 0022-0396 publication_status: published publisher: Elsevier BV status: public title: L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux type: journal_article user_id: '31496' volume: 400 year: '2024' ... --- _id: '57820' article_number: '113600' author: - first_name: Vanja full_name: Nikolić, Vanja last_name: Nikolić - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: ama: Nikolić V, Winkler M. L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation. Nonlinear Analysis. 2024;247. doi:10.1016/j.na.2024.113600 apa: Nikolić, V., & Winkler, M. (2024). L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation. Nonlinear Analysis, 247, Article 113600. https://doi.org/10.1016/j.na.2024.113600 bibtex: '@article{Nikolić_Winkler_2024, title={L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation}, volume={247}, DOI={10.1016/j.na.2024.113600}, number={113600}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Nikolić, Vanja and Winkler, Michael}, year={2024} }' chicago: Nikolić, Vanja, and Michael Winkler. “L∞ Blow-up in the Jordan-Moore-Gibson-Thompson Equation.” Nonlinear Analysis 247 (2024). https://doi.org/10.1016/j.na.2024.113600. ieee: 'V. Nikolić and M. Winkler, “L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation,” Nonlinear Analysis, vol. 247, Art. no. 113600, 2024, doi: 10.1016/j.na.2024.113600.' mla: Nikolić, Vanja, and Michael Winkler. “L∞ Blow-up in the Jordan-Moore-Gibson-Thompson Equation.” Nonlinear Analysis, vol. 247, 113600, Elsevier BV, 2024, doi:10.1016/j.na.2024.113600. short: V. Nikolić, M. Winkler, Nonlinear Analysis 247 (2024). date_created: 2024-12-18T07:13:19Z date_updated: 2026-01-05T08:02:36Z department: - _id: '90' doi: 10.1016/j.na.2024.113600 intvolume: ' 247' language: - iso: eng project: - _id: '245' name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)' publication: Nonlinear Analysis publication_identifier: issn: - 0362-546X publication_status: published publisher: Elsevier BV status: public title: L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation type: journal_article user_id: '11829' volume: 247 year: '2024' ... --- _id: '63285' author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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} }' 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. 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.' 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). date_created: 2025-12-18T19:18:31Z date_updated: 2025-12-18T20:07:12Z doi: 10.57262/ade028-1112-921 intvolume: ' 28' issue: 11/12 language: - iso: eng publication: Advances in Differential Equations publication_identifier: issn: - 1079-9389 publication_status: published publisher: Khayyam Publishing, Inc status: public title: Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing type: journal_article user_id: '31496' volume: 28 year: '2023' ... --- _id: '63288' abstract: - lang: eng 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 ." article_number: '20220578' author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler 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 apa: Winkler, M. (2023). Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. Open Mathematics, 21(1), Article 20220578. https://doi.org/10.1515/math-2022-0578 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={120220578}, journal={Open Mathematics}, publisher={Walter de Gruyter GmbH}, author={Winkler, Michael}, year={2023} }' 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. ieee: 'M. Winkler, “Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type,” Open Mathematics, vol. 21, no. 1, Art. no. 20220578, 2023, doi: 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, 20220578, Walter de Gruyter GmbH, 2023, doi:10.1515/math-2022-0578. short: M. Winkler, Open Mathematics 21 (2023). date_created: 2025-12-18T19:19:35Z date_updated: 2025-12-18T20:07:34Z doi: 10.1515/math-2022-0578 intvolume: ' 21' issue: '1' language: - iso: eng publication: Open Mathematics publication_identifier: issn: - 2391-5455 publication_status: published publisher: Walter de Gruyter GmbH status: public title: Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type type: journal_article user_id: '31496' volume: 21 year: '2023' ... --- _id: '63287' abstract: - lang: eng 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." author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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.' 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. date_created: 2025-12-18T19:19:13Z date_updated: 2025-12-18T20:07:25Z doi: 10.1007/s41808-023-00230-y intvolume: ' 9' issue: '2' language: - iso: eng page: 919-959 publication: Journal of Elliptic and Parabolic Equations publication_identifier: issn: - 2296-9020 - 2296-9039 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity type: journal_article user_id: '31496' volume: 9 year: '2023' ... --- _id: '63289' author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler - first_name: Tomomi full_name: Yokota, Tomomi last_name: Yokota citation: 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 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 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} }' 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.' 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.' 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. date_created: 2025-12-18T19:19:57Z date_updated: 2025-12-18T20:07:42Z doi: 10.1016/j.jde.2023.07.029 intvolume: ' 374' language: - iso: eng page: 1-28 publication: Journal of Differential Equations publication_identifier: issn: - 0022-0396 publication_status: published publisher: Elsevier BV status: public title: Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems type: journal_article user_id: '31496' volume: 374 year: '2023' ... --- _id: '63271' 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. author: - first_name: Youshan full_name: Tao, Youshan last_name: Tao - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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.' 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. date_created: 2025-12-18T19:12:35Z date_updated: 2025-12-18T20:10:55Z doi: 10.1142/s0218202523500045 intvolume: ' 33' issue: '01' language: - iso: eng page: 103-138 publication: Mathematical Models and Methods in Applied Sciences publication_identifier: issn: - 0218-2025 - 1793-6314 publication_status: published publisher: World Scientific Pub Co Pte Ltd status: public title: Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers type: journal_article user_id: '31496' volume: 33 year: '2023' ... --- _id: '63267' article_number: '180' author: - first_name: Jaewook full_name: Ahn, Jaewook last_name: Ahn - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler 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 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 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} }' 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. short: J. Ahn, M. Winkler, Calculus of Variations and Partial Differential Equations 62 (2023). date_created: 2025-12-18T19:10:55Z date_updated: 2025-12-18T20:10:21Z doi: 10.1007/s00526-023-02523-5 intvolume: ' 62' issue: '6' language: - iso: eng publication: Calculus of Variations and Partial Differential Equations publication_identifier: issn: - 0944-2669 - 1432-0835 publication_status: published publisher: Springer Science and Business Media LLC status: public title: A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system type: journal_article user_id: '31496' volume: 62 year: '2023' ... --- _id: '63270' author: - first_name: Genglin full_name: Li, Genglin last_name: Li - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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.' 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. short: G. Li, M. Winkler, Communications in Mathematical Sciences 21 (2023) 299–322. date_created: 2025-12-18T19:12:01Z date_updated: 2025-12-18T20:10:48Z doi: 10.4310/cms.2023.v21.n2.a1 intvolume: ' 21' issue: '2' language: - iso: eng page: 299-322 publication: Communications in Mathematical Sciences publication_identifier: issn: - 1539-6746 - 1945-0796 publication_status: published publisher: International Press of Boston status: public title: Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities type: journal_article user_id: '31496' volume: 21 year: '2023' ... --- _id: '63273' article_number: '103820' author: - first_name: Youshan full_name: Tao, Youshan last_name: Tao - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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' 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' 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} }' 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.' 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.' 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).' date_created: 2025-12-18T19:13:40Z date_updated: 2025-12-18T20:11:09Z doi: 10.1016/j.nonrwa.2022.103820 intvolume: ' 71' language: - iso: eng publication: 'Nonlinear Analysis: Real World Applications' publication_identifier: issn: - 1468-1218 publication_status: published publisher: Elsevier BV status: public title: Analysis of a chemotaxis-SIS epidemic model with unbounded infection force type: journal_article user_id: '31496' volume: 71 year: '2023' ... --- _id: '63281' abstract: - lang: eng text: AbstractA no-flux initial-boundary value problem for

ut=Δ(uϕ(v)),vt=Δv−uv,(⋆)

is considered in smoothly bounded subdomains of

with

n⩾1

and suitably regular initial data, whereφis assumed to reflect algebraic type cross-degeneracies by sharing essential features with

0⩽ξ↦ξα

for some

α⩾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 profile

u∞

and some null set

N⋆⊂(0,∞)

, a corresponding global generalized solution, known to exist according to recent literature, satisfies

ρ(u(⋅,t))⇀⋆ρ(u∞)in L∞(Ω) and v(⋅,t)→0in Lp(Ω)for all p⩾1

(0,∞)∖N⋆∋t→∞

, where

ρ(ξ):=ξ2(ξ+1)2

ξ⩾0

. In the particular case when either

n⩽2

and

α⩾1

is arbitrary, or

n⩾1

and

α∈[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. author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler 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 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 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} }' 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.' 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. short: M. Winkler, Nonlinearity 36 (2023) 4438–4469. date_created: 2025-12-18T19:17:01Z date_updated: 2025-12-18T20:12:06Z doi: 10.1088/1361-6544/ace22e intvolume: ' 36' issue: '8' language: - iso: eng page: 4438-4469 publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published publisher: IOP Publishing status: public title: Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction type: journal_article user_id: '31496' volume: 36 year: '2023' ... --- _id: '63276' abstract: - lang: eng 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." author: - first_name: Yu full_name: Tian, Yu last_name: Tian - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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. short: Y. Tian, M. Winkler, Mathematical Methods in the Applied Sciences 46 (2023) 15667–15683. date_created: 2025-12-18T19:15:06Z date_updated: 2025-12-18T20:11:29Z doi: 10.1002/mma.9419 intvolume: ' 46' issue: '14' language: - iso: eng page: 15667-15683 publication: Mathematical Methods in the Applied Sciences publication_identifier: issn: - 0170-4214 - 1099-1476 publication_status: published publisher: Wiley status: public title: Keller–Segel–Stokes interaction involving signal‐dependent motilities type: journal_article user_id: '31496' volume: 46 year: '2023' ... --- _id: '63275' author: - first_name: Youshan full_name: Tao, Youshan last_name: Tao - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: ama: Tao Y, Winkler M. Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities. Evolution Equations and Control Theory. 2023;12(6):1676-1687. doi:10.3934/eect.2023031 apa: Tao, Y., & Winkler, M. (2023). Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities. Evolution Equations and Control Theory, 12(6), 1676–1687. https://doi.org/10.3934/eect.2023031 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={10.3934/eect.2023031}, 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} }' chicago: 'Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” Evolution Equations and Control Theory 12, no. 6 (2023): 1676–87. https://doi.org/10.3934/eect.2023031.' ieee: 'Y. Tao and M. Winkler, “Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities,” Evolution Equations and Control Theory, vol. 12, no. 6, pp. 1676–1687, 2023, doi: 10.3934/eect.2023031.' mla: Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” Evolution Equations and Control Theory, vol. 12, no. 6, American Institute of Mathematical Sciences (AIMS), 2023, pp. 1676–87, doi:10.3934/eect.2023031. short: Y. Tao, M. Winkler, Evolution Equations and Control Theory 12 (2023) 1676–1687. date_created: 2025-12-18T19:14:46Z date_updated: 2025-12-18T20:11:23Z doi: 10.3934/eect.2023031 intvolume: ' 12' issue: '6' language: - iso: eng page: 1676-1687 publication: Evolution Equations and Control Theory publication_identifier: issn: - 2163-2480 publication_status: published publisher: American Institute of Mathematical Sciences (AIMS) status: public title: Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities type: journal_article user_id: '31496' volume: 12 year: '2023' ... --- _id: '63277' author: - first_name: Kevin J. full_name: Painter, Kevin J. last_name: Painter - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler 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 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} }' 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.' 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.' 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. short: K.J. Painter, M. Winkler, SIAM Journal on Applied Mathematics 83 (2023) 2096–2117. date_created: 2025-12-18T19:15:29Z date_updated: 2025-12-18T20:11:36Z doi: 10.1137/22m1539393 intvolume: ' 83' issue: '5' language: - iso: eng page: 2096-2117 publication: SIAM Journal on Applied Mathematics publication_identifier: issn: - 0036-1399 - 1095-712X publication_status: published publisher: Society for Industrial & Applied Mathematics (SIAM) status: public title: Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities type: journal_article user_id: '31496' volume: 83 year: '2023' ... --- _id: '63283' abstract: - lang: eng text: "AbstractThe parabolic problem

$$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t=\\Delta \\big (u\\phi (v)\\big ), \\\\ v_t=\\Delta v-uv, \\end{array} \\right. \\end{aligned}$$

\r\n \ \r\n \r\n \r\n \ \r\n \r\n \ \r\n \r\n \ \r\n \r\n \ \r\n \r\n \ u\r\n t\r\n \ \r\n =\r\n \ Δ\r\n \r\n \ (\r\n \r\n \ u\r\n ϕ\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 \r\n \ \r\n \r\n \ \r\n \r\n \ \r\n v\r\n \ t\r\n \r\n \ =\r\n Δ\r\n \ v\r\n -\r\n \ u\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 \r\n \ is considered in smoothly bounded subdomains of

$${\\mathbb {R}}^n$$

\r\n \ \r\n \r\n R\r\n \ \r\n n\r\n \ \r\n with arbitrary

$$n\\ge 1$$

\r\n \ \r\n n\r\n ≥\r\n \ 1\r\n \r\n . Under the assumptions that

$$\\phi \\in C^0([0,\\infty )) \\cap C^3((0,\\infty ))$$

\r\n \ \r\n ϕ\r\n ∈\r\n \ \r\n C\r\n \ 0\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 ∩\r\n \ \r\n C\r\n \ 3\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 \r\n is positive on

$$(0,\\infty )$$

\r\n \ \r\n (\r\n 0\r\n \ ,\r\n ∞\r\n \ )\r\n \r\n and satisfies

$$\\begin{aligned} \\liminf _{\\xi \\searrow 0} \\frac{\\phi (\\xi )}{\\xi ^\\alpha }>0 \\quad {\\text{ and }} \\quad \\limsup _{\\xi \\searrow 0} \\big \\{ \\xi ^\\beta |\\phi '(\\xi )| \\big \\}<\\infty \\end{aligned}$$

\r\n \ \r\n \r\n \r\n \ \r\n \r\n \ \r\n lim inf\r\n \r\n ξ\r\n \ ↘\r\n 0\r\n \ \r\n \r\n \ \r\n \r\n \ ϕ\r\n (\r\n \ ξ\r\n )\r\n \ \r\n \r\n \ ξ\r\n α\r\n \ \r\n \r\n \ >\r\n 0\r\n \ \r\n \r\n \ \r\n and\r\n \ \r\n \r\n \ \r\n \r\n \ lim sup\r\n \r\n \ ξ\r\n ↘\r\n \ 0\r\n \r\n \ \r\n \r\n \ {\r\n \r\n \ \r\n ξ\r\n \ β\r\n \r\n \ \r\n |\r\n \ \r\n ϕ\r\n \ ′\r\n \r\n \ \r\n (\r\n \ ξ\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 some

$$\\alpha >0$$

\r\n \ \r\n α\r\n >\r\n \ 0\r\n \r\n and

$$\\beta >0$$

\r\n \r\n \ β\r\n >\r\n \ 0\r\n \r\n , 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

$$\\alpha =0$$

\r\n \ \r\n α\r\n =\r\n \ 0\r\n \r\n and

$$\\alpha \\in (0,2)$$

\r\n \r\n \ α\r\n ∈\r\n \ (\r\n 0\r\n \ ,\r\n 2\r\n \ )\r\n \r\n , or were restricted to low-dimensional settings by requiring that

$$n\\le 2$$

\r\n \ \r\n n\r\n ≤\r\n \ 2\r\n \r\n ." article_number: '32' author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: ama: Winkler M. Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction. Zeitschrift für angewandte Mathematik und Physik. 2023;74(1). doi:10.1007/s00033-022-01925-3 apa: Winkler, M. (2023). Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction. Zeitschrift Für Angewandte Mathematik Und Physik, 74(1), Article 32. https://doi.org/10.1007/s00033-022-01925-3 bibtex: '@article{Winkler_2023, title={Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction}, volume={74}, DOI={10.1007/s00033-022-01925-3}, 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.” Zeitschrift Für Angewandte Mathematik Und Physik 74, no. 1 (2023). https://doi.org/10.1007/s00033-022-01925-3. ieee: 'M. Winkler, “Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction,” Zeitschrift für angewandte Mathematik und Physik, vol. 74, no. 1, Art. no. 32, 2023, doi: 10.1007/s00033-022-01925-3.' mla: Winkler, Michael. “Global Generalized Solvability in a Strongly Degenerate Taxis-Type Parabolic System Modeling Migration–Consumption Interaction.” Zeitschrift Für Angewandte Mathematik Und Physik, vol. 74, no. 1, 32, Springer Science and Business Media LLC, 2023, doi:10.1007/s00033-022-01925-3. short: M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 74 (2023). date_created: 2025-12-18T19:17:51Z date_updated: 2025-12-18T20:12:20Z doi: 10.1007/s00033-022-01925-3 intvolume: ' 74' issue: '1' language: - iso: eng publication: Zeitschrift für angewandte Mathematik und Physik publication_identifier: issn: - 0044-2275 - 1420-9039 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction type: journal_article user_id: '31496' volume: 74 year: '2023' ... --- _id: '63255' author: - first_name: Genglin full_name: Li, Genglin last_name: Li - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: ama: Li G, Winkler M. Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities. Applicable Analysis. 2023;103(1):45-64. doi:10.1080/00036811.2023.2173183 apa: Li, G., & Winkler, M. (2023). Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities. Applicable Analysis, 103(1), 45–64. https://doi.org/10.1080/00036811.2023.2173183 bibtex: '@article{Li_Winkler_2023, title={Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities}, volume={103}, DOI={10.1080/00036811.2023.2173183}, number={1}, journal={Applicable Analysis}, publisher={Informa UK Limited}, author={Li, Genglin and Winkler, Michael}, year={2023}, pages={45–64} }' chicago: 'Li, Genglin, and Michael Winkler. “Refined Regularity Analysis for a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Applicable Analysis 103, no. 1 (2023): 45–64. https://doi.org/10.1080/00036811.2023.2173183.' ieee: 'G. Li and M. Winkler, “Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities,” Applicable Analysis, vol. 103, no. 1, pp. 45–64, 2023, doi: 10.1080/00036811.2023.2173183.' mla: Li, Genglin, and Michael Winkler. “Refined Regularity Analysis for a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Applicable Analysis, vol. 103, no. 1, Informa UK Limited, 2023, pp. 45–64, doi:10.1080/00036811.2023.2173183. short: G. Li, M. Winkler, Applicable Analysis 103 (2023) 45–64. date_created: 2025-12-18T19:05:34Z date_updated: 2025-12-18T20:14:04Z doi: 10.1080/00036811.2023.2173183 intvolume: ' 103' issue: '1' language: - iso: eng page: 45-64 publication: Applicable Analysis publication_identifier: issn: - 0003-6811 - 1563-504X publication_status: published publisher: Informa UK Limited status: public title: Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities type: journal_article user_id: '31496' volume: 103 year: '2023' ... --- _id: '63261' abstract: - lang: eng text: "\r\n The taxis-type migration–consumption model accounting for signal-dependent motilities, as given by \r\n \r\n \ u_{t} = \\Delta (u\\phi(v))\r\n \r\n \ , \r\n \r\n v_{t} = \\Delta v-uv\r\n \r\n , is considered for suitably smooth functions \r\n \r\n \ \\phi\\colon[0,\\infty)\\to\\R\r\n \ \r\n which are such that \r\n \r\n \ \\phi>0\r\n \r\n \ on \r\n \r\n (0,\\infty)\r\n \ \r\n , but that in addition \r\n \ \r\n \\phi(0)=0\r\n \ \r\n with \r\n \r\n \ \\phi'(0)>0\r\n \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 \r\n V_{t} = \\Delta V + \\nabla\\cdot ( a(x,t)V) + b(x,t)V\r\n \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 \r\n a\r\n \ \r\n and \r\n \r\n \ b\r\n \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 \ " author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: ama: Winkler M. A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. 2023;41(1):95-127. doi:10.4171/aihpc/73 apa: Winkler, M. (2023). A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, 41(1), 95–127. https://doi.org/10.4171/aihpc/73 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={10.4171/aihpc/73}, 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} }' chicago: 'Winkler, Michael. “A Quantitative Strong Parabolic Maximum Principle and Application to a Taxis-Type Migration–Consumption Model Involving Signal-Dependent Degenerate Diffusion.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 41, no. 1 (2023): 95–127. https://doi.org/10.4171/aihpc/73.' ieee: 'M. Winkler, “A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion,” Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 41, no. 1, pp. 95–127, 2023, doi: 10.4171/aihpc/73.' mla: Winkler, Michael. “A Quantitative Strong Parabolic Maximum Principle and Application to a Taxis-Type Migration–Consumption Model Involving Signal-Dependent Degenerate Diffusion.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, vol. 41, no. 1, European Mathematical Society - EMS - Publishing House GmbH, 2023, pp. 95–127, doi:10.4171/aihpc/73. short: M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 41 (2023) 95–127. date_created: 2025-12-18T19:08:10Z date_updated: 2025-12-18T20:14:52Z doi: 10.4171/aihpc/73 intvolume: ' 41' issue: '1' language: - iso: eng page: 95-127 publication: Annales de l'Institut Henri Poincaré C, Analyse non linéaire publication_identifier: issn: - 0294-1449 - 1873-1430 publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion type: journal_article user_id: '31496' volume: 41 year: '2023' ...