[{"status":"public","type":"journal_article","publication":"Nonlinear Analysis","language":[{"iso":"eng"}],"article_number":"113600","user_id":"31496","_id":"63256","citation":{"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","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).","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} }","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","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."},"intvolume":" 247","year":"2024","publication_status":"published","publication_identifier":{"issn":["0362-546X"]},"doi":"10.1016/j.na.2024.113600","title":"L∞ blow-up in the Jordan–Moore–Gibson–Thompson equation","date_created":"2025-12-18T19:06:09Z","author":[{"first_name":"Vanja","full_name":"Nikolić, Vanja","last_name":"Nikolić"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"volume":247,"date_updated":"2025-12-18T20:14:12Z","publisher":"Elsevier BV"},{"language":[{"iso":"eng"}],"user_id":"31496","_id":"63260","status":"public","abstract":[{"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","lang":"eng"}],"publication":"Mathematische Nachrichten","type":"journal_article","doi":"10.1002/mana.202300361","title":"A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities","volume":297,"date_created":"2025-12-18T19:07:48Z","author":[{"last_name":"Wang","full_name":"Wang, Yulan","first_name":"Yulan"},{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_updated":"2025-12-18T20:14:46Z","publisher":"Wiley","intvolume":" 297","page":"2353-2364","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","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.","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.","short":"Y. Wang, M. Winkler, Mathematische Nachrichten 297 (2024) 2353–2364.","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} }","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.","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"},"year":"2024","issue":"6","publication_identifier":{"issn":["0025-584X","1522-2616"]},"publication_status":"published"},{"abstract":[{"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.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Israel Journal of Mathematics","language":[{"iso":"eng"}],"_id":"63262","user_id":"31496","year":"2024","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","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.","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.","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","short":"M. Winkler, Israel Journal of Mathematics 263 (2024) 93–127.","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} }","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."},"page":"93-127","intvolume":" 263","publication_status":"published","publication_identifier":{"issn":["0021-2172","1565-8511"]},"issue":"1","title":"Complete infinite-time mass aggregation in a quasilinear Keller–Segel system","doi":"10.1007/s11856-024-2618-9","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:14:59Z","date_created":"2025-12-18T19:08:34Z","author":[{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"volume":263},{"status":"public","publication":"Journal of Differential Equations","type":"journal_article","language":[{"iso":"eng"}],"_id":"63263","user_id":"31496","year":"2024","intvolume":" 400","page":"423-456","citation":{"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","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.","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.","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"},"publication_identifier":{"issn":["0022-0396"]},"publication_status":"published","title":"L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux","doi":"10.1016/j.jde.2024.04.028","publisher":"Elsevier BV","date_updated":"2025-12-18T20:15:05Z","volume":400,"date_created":"2025-12-18T19:09:07Z","author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}]},{"status":"public","type":"journal_article","publication":"Nonlinear Analysis","article_number":"113600","language":[{"iso":"eng"}],"project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"_id":"57820","user_id":"11829","department":[{"_id":"90"}],"year":"2024","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","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.","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.","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.","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} }","short":"V. Nikolić, M. Winkler, Nonlinear Analysis 247 (2024).","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"},"intvolume":" 247","publication_status":"published","publication_identifier":{"issn":["0362-546X"]},"title":"L∞ blow-up in the Jordan-Moore-Gibson-Thompson equation","doi":"10.1016/j.na.2024.113600","publisher":"Elsevier BV","date_updated":"2026-01-05T08:02:36Z","author":[{"first_name":"Vanja","last_name":"Nikolić","full_name":"Nikolić, Vanja"},{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2024-12-18T07:13:19Z","volume":247},{"intvolume":" 28","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","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.","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} }","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.","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"},"year":"2023","issue":"11/12","publication_identifier":{"issn":["1079-9389"]},"publication_status":"published","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","volume":28,"author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"date_created":"2025-12-18T19:18:31Z","date_updated":"2025-12-18T20:07:12Z","publisher":"Khayyam Publishing, Inc","status":"public","publication":"Advances in Differential Equations","type":"journal_article","language":[{"iso":"eng"}],"user_id":"31496","_id":"63285"},{"date_created":"2025-12-18T19:19:35Z","author":[{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"volume":21,"date_updated":"2025-12-18T20:07:34Z","publisher":"Walter de Gruyter GmbH","doi":"10.1515/math-2022-0578","title":"Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type","issue":"1","publication_status":"published","publication_identifier":{"issn":["2391-5455"]},"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, Art. no. 20220578, 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.","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} }","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).","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"},"intvolume":" 21","year":"2023","user_id":"31496","_id":"63288","language":[{"iso":"eng"}],"article_number":"20220578","type":"journal_article","publication":"Open Mathematics","status":"public","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 ."}]},{"title":"Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity","doi":"10.1007/s41808-023-00230-y","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:07:25Z","volume":9,"author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"date_created":"2025-12-18T19:19:13Z","year":"2023","page":"919-959","intvolume":" 9","citation":{"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.","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} }","short":"M. Winkler, Journal of Elliptic and Parabolic Equations 9 (2023) 919–959.","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","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","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."},"publication_identifier":{"issn":["2296-9020","2296-9039"]},"publication_status":"published","issue":"2","language":[{"iso":"eng"}],"_id":"63287","user_id":"31496","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."}],"status":"public","publication":"Journal of Elliptic and Parabolic Equations","type":"journal_article"},{"date_updated":"2025-12-18T20:07:42Z","publisher":"Elsevier BV","author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"},{"first_name":"Tomomi","last_name":"Yokota","full_name":"Yokota, Tomomi"}],"date_created":"2025-12-18T19:19:57Z","volume":374,"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_status":"published","publication_identifier":{"issn":["0022-0396"]},"year":"2023","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","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.","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} }","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.","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"},"page":"1-28","intvolume":" 374","_id":"63289","user_id":"31496","language":[{"iso":"eng"}],"type":"journal_article","publication":"Journal of Differential Equations","status":"public"},{"_id":"63271","user_id":"31496","language":[{"iso":"eng"}],"type":"journal_article","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. "}],"status":"public","publisher":"World Scientific Pub Co Pte Ltd","date_updated":"2025-12-18T20:10:55Z","author":[{"first_name":"Youshan","full_name":"Tao, Youshan","last_name":"Tao"},{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"date_created":"2025-12-18T19:12:35Z","volume":33,"title":"Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers","doi":"10.1142/s0218202523500045","publication_status":"published","publication_identifier":{"issn":["0218-2025","1793-6314"]},"issue":"01","year":"2023","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","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.","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.","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} }","short":"Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 33 (2023) 103–138.","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"},"page":"103-138","intvolume":" 33"},{"article_number":"180","language":[{"iso":"eng"}],"_id":"63267","user_id":"31496","status":"public","publication":"Calculus of Variations and Partial Differential Equations","type":"journal_article","title":"A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system","doi":"10.1007/s00526-023-02523-5","date_updated":"2025-12-18T20:10:21Z","publisher":"Springer Science and Business Media LLC","volume":62,"date_created":"2025-12-18T19:10:55Z","author":[{"first_name":"Jaewook","last_name":"Ahn","full_name":"Ahn, Jaewook"},{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"year":"2023","intvolume":" 62","citation":{"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} }","short":"J. Ahn, M. Winkler, Calculus of Variations and Partial Differential Equations 62 (2023).","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.","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.","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"},"publication_identifier":{"issn":["0944-2669","1432-0835"]},"publication_status":"published","issue":"6"},{"language":[{"iso":"eng"}],"_id":"63270","user_id":"31496","status":"public","type":"journal_article","publication":"Communications in Mathematical Sciences","title":"Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities","doi":"10.4310/cms.2023.v21.n2.a1","publisher":"International Press of Boston","date_updated":"2025-12-18T20:10:48Z","author":[{"full_name":"Li, Genglin","last_name":"Li","first_name":"Genglin"},{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"date_created":"2025-12-18T19:12:01Z","volume":21,"year":"2023","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","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} }","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.","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."},"page":"299-322","intvolume":" 21","publication_status":"published","publication_identifier":{"issn":["1539-6746","1945-0796"]},"issue":"2"},{"year":"2023","intvolume":" 71","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","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.","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} }","short":"Y. Tao, M. Winkler, Nonlinear Analysis: Real World Applications 71 (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."},"publication_identifier":{"issn":["1468-1218"]},"publication_status":"published","title":"Analysis of a chemotaxis-SIS epidemic model with unbounded infection force","doi":"10.1016/j.nonrwa.2022.103820","publisher":"Elsevier BV","date_updated":"2025-12-18T20:11:09Z","volume":71,"author":[{"first_name":"Youshan","last_name":"Tao","full_name":"Tao, Youshan"},{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:13:40Z","status":"public","publication":"Nonlinear Analysis: Real World Applications","type":"journal_article","article_number":"103820","language":[{"iso":"eng"}],"_id":"63273","user_id":"31496"},{"doi":"10.1088/1361-6544/ace22e","title":"Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction","date_created":"2025-12-18T19:17:01Z","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"volume":36,"date_updated":"2025-12-18T20:12:06Z","publisher":"IOP Publishing","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.","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.","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} }","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"},"intvolume":" 36","page":"4438-4469","year":"2023","issue":"8","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"language":[{"iso":"eng"}],"user_id":"31496","_id":"63281","status":"public","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"}],"type":"journal_article","publication":"Nonlinearity"},{"language":[{"iso":"eng"}],"user_id":"31496","_id":"63276","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"}],"type":"journal_article","publication":"Mathematical Methods in the Applied Sciences","doi":"10.1002/mma.9419","title":"Keller–Segel–Stokes interaction involving signal‐dependent motilities","author":[{"full_name":"Tian, Yu","last_name":"Tian","first_name":"Yu"},{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-18T19:15:06Z","volume":46,"publisher":"Wiley","date_updated":"2025-12-18T20:11:29Z","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","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.","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","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.","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} }","short":"Y. Tian, M. Winkler, Mathematical Methods in the Applied Sciences 46 (2023) 15667–15683."},"page":"15667-15683","intvolume":" 46","year":"2023","issue":"14","publication_status":"published","publication_identifier":{"issn":["0170-4214","1099-1476"]}},{"title":"Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities","doi":"10.3934/eect.2023031","date_updated":"2025-12-18T20:11:23Z","publisher":"American Institute of Mathematical Sciences (AIMS)","volume":12,"author":[{"full_name":"Tao, Youshan","last_name":"Tao","first_name":"Youshan"},{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"date_created":"2025-12-18T19:14:46Z","year":"2023","page":"1676-1687","intvolume":" 12","citation":{"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} }","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.","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.","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"},"publication_identifier":{"issn":["2163-2480"]},"publication_status":"published","issue":"6","language":[{"iso":"eng"}],"_id":"63275","user_id":"31496","status":"public","publication":"Evolution Equations and Control Theory","type":"journal_article"},{"status":"public","publication":"SIAM Journal on Applied Mathematics","type":"journal_article","language":[{"iso":"eng"}],"_id":"63277","user_id":"31496","year":"2023","intvolume":" 83","page":"2096-2117","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","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.","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","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.","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} }"},"publication_identifier":{"issn":["0036-1399","1095-712X"]},"publication_status":"published","issue":"5","title":"Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities","doi":"10.1137/22m1539393","publisher":"Society for Industrial & Applied Mathematics (SIAM)","date_updated":"2025-12-18T20:11:36Z","volume":83,"date_created":"2025-12-18T19:15:29Z","author":[{"last_name":"Painter","full_name":"Painter, Kevin J.","first_name":"Kevin J."},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}]},{"title":"Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction","doi":"10.1007/s00033-022-01925-3","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:12:20Z","volume":74,"author":[{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2025-12-18T19:17:51Z","year":"2023","intvolume":" 74","citation":{"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","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.","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} }","short":"M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 74 (2023).","ama":"Winkler M. Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction. Zeitschrift für angewandte Mathematik und Physik. 2023;74(1). doi: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.","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."},"publication_identifier":{"issn":["0044-2275","1420-9039"]},"publication_status":"published","issue":"1","article_number":"32","language":[{"iso":"eng"}],"_id":"63283","user_id":"31496","abstract":[{"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 .","lang":"eng"}],"status":"public","publication":"Zeitschrift für angewandte Mathematik und Physik","type":"journal_article"},{"volume":103,"date_created":"2025-12-18T19:05:34Z","author":[{"full_name":"Li, Genglin","last_name":"Li","first_name":"Genglin"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"publisher":"Informa UK Limited","date_updated":"2025-12-18T20:14:04Z","doi":"10.1080/00036811.2023.2173183","title":"Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities","issue":"1","publication_identifier":{"issn":["0003-6811","1563-504X"]},"publication_status":"published","page":"45-64","intvolume":" 103","citation":{"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.","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.","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","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} }","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.","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"},"year":"2023","user_id":"31496","_id":"63255","language":[{"iso":"eng"}],"publication":"Applicable Analysis","type":"journal_article","status":"public"},{"publisher":"European Mathematical Society - EMS - Publishing House GmbH","date_updated":"2025-12-18T20:14:52Z","volume":41,"author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:08:10Z","title":"A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion","doi":"10.4171/aihpc/73","publication_identifier":{"issn":["0294-1449","1873-1430"]},"publication_status":"published","issue":"1","year":"2023","page":"95-127","intvolume":" 41","citation":{"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.","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.","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","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 41 (2023) 95–127.","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} }","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.","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"},"_id":"63261","user_id":"31496","language":[{"iso":"eng"}],"publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","type":"journal_article","abstract":[{"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 ","lang":"eng"}],"status":"public"}]