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Tao, M. Winkler, Evolution Equations and Control Theory 12 (2023) 1676–1687.","ieee":"Y. Tao and M. Winkler, “Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities,” <i>Evolution Equations and Control Theory</i>, vol. 12, no. 6, pp. 1676–1687, 2023, doi: <a href=\"https://doi.org/10.3934/eect.2023031\">10.3934/eect.2023031</a>.","chicago":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” <i>Evolution Equations and Control Theory</i> 12, no. 6 (2023): 1676–87. <a href=\"https://doi.org/10.3934/eect.2023031\">https://doi.org/10.3934/eect.2023031</a>.","ama":"Tao Y, Winkler M. Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities. <i>Evolution Equations and Control Theory</i>. 2023;12(6):1676-1687. doi:<a href=\"https://doi.org/10.3934/eect.2023031\">10.3934/eect.2023031</a>"},"page":"1676-1687","intvolume":"        12","year":"2023","user_id":"31496","_id":"53317","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Control and Optimization","Modeling and Simulation"],"type":"journal_article","publication":"Evolution Equations and Control Theory","status":"public"},{"doi":"10.4171/aihpc/73","title":"A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion","author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2024-04-07T12:34:35Z","date_updated":"2024-04-07T12:36:00Z","publisher":"European Mathematical Society - EMS - Publishing House GmbH","citation":{"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}, DOI={<a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>}, journal={Annales de l’Institut Henri Poincaré C, Analyse non linéaire}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Winkler, Michael}, year={2023} }","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire (2023).","mla":"Winkler, Michael. “A Quantitative Strong Parabolic Maximum Principle and Application to a Taxis-Type Migration–Consumption Model Involving Signal-Dependent Degenerate Diffusion.” <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>, European Mathematical Society - EMS - Publishing House GmbH, 2023, doi:<a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>.","apa":"Winkler, M. (2023). A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion. <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>. <a href=\"https://doi.org/10.4171/aihpc/73\">https://doi.org/10.4171/aihpc/73</a>","ama":"Winkler M. A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion. <i>Annales de l’Institut Henri Poincaré C, Analyse non linéaire</i>. Published online 2023. doi:<a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>","ieee":"M. Winkler, “A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion,” <i>Annales de l’Institut Henri Poincaré C, Analyse non linéaire</i>, 2023, doi: <a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>.","chicago":"Winkler, Michael. “A Quantitative Strong Parabolic Maximum Principle and Application to a Taxis-Type Migration–Consumption Model Involving Signal-Dependent Degenerate Diffusion.” <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>, 2023. <a href=\"https://doi.org/10.4171/aihpc/73\">https://doi.org/10.4171/aihpc/73</a>."},"year":"2023","publication_identifier":{"issn":["0294-1449","1873-1430"]},"publication_status":"published","language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Analysis","Applied Mathematics"],"user_id":"31496","_id":"53320","status":"public","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","type":"journal_article"},{"status":"public","type":"journal_article","publication":"Applicable Analysis","keyword":["Applied Mathematics","Analysis"],"language":[{"iso":"eng"}],"_id":"53318","user_id":"31496","year":"2023","citation":{"ama":"Li G, Winkler M. Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities. <i>Applicable Analysis</i>. 2023;103(1):45-64. doi:<a href=\"https://doi.org/10.1080/00036811.2023.2173183\">10.1080/00036811.2023.2173183</a>","ieee":"G. Li and M. Winkler, “Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities,” <i>Applicable Analysis</i>, vol. 103, no. 1, pp. 45–64, 2023, doi: <a href=\"https://doi.org/10.1080/00036811.2023.2173183\">10.1080/00036811.2023.2173183</a>.","chicago":"Li, Genglin, and Michael Winkler. “Refined Regularity Analysis for a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” <i>Applicable Analysis</i> 103, no. 1 (2023): 45–64. <a href=\"https://doi.org/10.1080/00036811.2023.2173183\">https://doi.org/10.1080/00036811.2023.2173183</a>.","short":"G. Li, M. Winkler, Applicable Analysis 103 (2023) 45–64.","mla":"Li, Genglin, and Michael Winkler. “Refined Regularity Analysis for a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” <i>Applicable Analysis</i>, vol. 103, no. 1, Informa UK Limited, 2023, pp. 45–64, doi:<a href=\"https://doi.org/10.1080/00036811.2023.2173183\">10.1080/00036811.2023.2173183</a>.","bibtex":"@article{Li_Winkler_2023, title={Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities}, volume={103}, DOI={<a href=\"https://doi.org/10.1080/00036811.2023.2173183\">10.1080/00036811.2023.2173183</a>}, number={1}, journal={Applicable Analysis}, publisher={Informa UK Limited}, author={Li, Genglin and Winkler, Michael}, year={2023}, pages={45–64} }","apa":"Li, G., &#38; Winkler, M. (2023). Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities. <i>Applicable Analysis</i>, <i>103</i>(1), 45–64. <a href=\"https://doi.org/10.1080/00036811.2023.2173183\">https://doi.org/10.1080/00036811.2023.2173183</a>"},"intvolume":"       103","page":"45-64","publication_status":"published","publication_identifier":{"issn":["0003-6811","1563-504X"]},"issue":"1","title":"Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities","doi":"10.1080/00036811.2023.2173183","publisher":"Informa UK Limited","date_updated":"2024-04-07T12:36:11Z","date_created":"2024-04-07T12:32:55Z","author":[{"last_name":"Li","full_name":"Li, Genglin","first_name":"Genglin"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"volume":103},{"publication_identifier":{"issn":["0218-2025","1793-6314"]},"publication_status":"published","intvolume":"        33","page":"103-138","citation":{"ieee":"Y. Tao and M. Winkler, “Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 33, no. 01, pp. 103–138, 2023, doi: <a href=\"https://doi.org/10.1142/s0218202523500045\">10.1142/s0218202523500045</a>.","chicago":"Tao, Youshan, and Michael Winkler. “Small-Signal Solutions to a Nonlocal Cross-Diffusion Model for Interaction of Scroungers with Rapidly Diffusing Foragers.” <i>Mathematical Models and Methods in Applied Sciences</i> 33, no. 01 (2023): 103–38. <a href=\"https://doi.org/10.1142/s0218202523500045\">https://doi.org/10.1142/s0218202523500045</a>.","ama":"Tao Y, Winkler M. Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. <i>Mathematical Models and Methods in Applied Sciences</i>. 2023;33(01):103-138. doi:<a href=\"https://doi.org/10.1142/s0218202523500045\">10.1142/s0218202523500045</a>","short":"Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 33 (2023) 103–138.","bibtex":"@article{Tao_Winkler_2023, title={Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers}, volume={33}, DOI={<a href=\"https://doi.org/10.1142/s0218202523500045\">10.1142/s0218202523500045</a>}, 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} }","mla":"Tao, Youshan, and Michael Winkler. “Small-Signal Solutions to a Nonlocal Cross-Diffusion Model for Interaction of Scroungers with Rapidly Diffusing Foragers.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 33, no. 01, World Scientific Pub Co Pte Ltd, 2023, pp. 103–38, doi:<a href=\"https://doi.org/10.1142/s0218202523500045\">10.1142/s0218202523500045</a>.","apa":"Tao, Y., &#38; Winkler, M. (2023). Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. <i>Mathematical Models and Methods in Applied Sciences</i>, <i>33</i>(01), 103–138. <a href=\"https://doi.org/10.1142/s0218202523500045\">https://doi.org/10.1142/s0218202523500045</a>"},"volume":33,"author":[{"full_name":"Tao, Youshan","last_name":"Tao","first_name":"Youshan"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_updated":"2024-04-07T12:43:17Z","doi":"10.1142/s0218202523500045","type":"journal_article","status":"public","user_id":"31496","_id":"53328","issue":"01","year":"2023","date_created":"2024-04-07T12:43:13Z","publisher":"World Scientific Pub Co Pte Ltd","title":"Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers","publication":"Mathematical Models and Methods in Applied Sciences","abstract":[{"lang":"eng","text":"<jats:p> 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. </jats:p>"}],"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Modeling and Simulation"]},{"article_number":"180","keyword":["Applied Mathematics","Analysis"],"language":[{"iso":"eng"}],"_id":"53324","user_id":"31496","status":"public","type":"journal_article","publication":"Calculus of Variations and Partial Differential Equations","title":"A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system","doi":"10.1007/s00526-023-02523-5","publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-07T12:40:06Z","author":[{"first_name":"Jaewook","full_name":"Ahn, Jaewook","last_name":"Ahn"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"date_created":"2024-04-07T12:40:02Z","volume":62,"year":"2023","citation":{"bibtex":"@article{Ahn_Winkler_2023, title={A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system}, volume={62}, DOI={<a href=\"https://doi.org/10.1007/s00526-023-02523-5\">10.1007/s00526-023-02523-5</a>}, 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.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 62, no. 6, 180, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s00526-023-02523-5\">10.1007/s00526-023-02523-5</a>.","apa":"Ahn, J., &#38; Winkler, M. (2023). A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system. <i>Calculus of Variations and Partial Differential Equations</i>, <i>62</i>(6), Article 180. <a href=\"https://doi.org/10.1007/s00526-023-02523-5\">https://doi.org/10.1007/s00526-023-02523-5</a>","chicago":"Ahn, Jaewook, and Michael Winkler. “A Critical Exponent for Blow-up in a Two-Dimensional Chemotaxis-Consumption System.” <i>Calculus of Variations and Partial Differential Equations</i> 62, no. 6 (2023). <a href=\"https://doi.org/10.1007/s00526-023-02523-5\">https://doi.org/10.1007/s00526-023-02523-5</a>.","ieee":"J. Ahn and M. Winkler, “A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 62, no. 6, Art. no. 180, 2023, doi: <a href=\"https://doi.org/10.1007/s00526-023-02523-5\">10.1007/s00526-023-02523-5</a>.","ama":"Ahn J, Winkler M. A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system. <i>Calculus of Variations and Partial Differential Equations</i>. 2023;62(6). doi:<a href=\"https://doi.org/10.1007/s00526-023-02523-5\">10.1007/s00526-023-02523-5</a>"},"intvolume":"        62","publication_status":"published","publication_identifier":{"issn":["0944-2669","1432-0835"]},"issue":"6"},{"title":"Analysis of a chemotaxis-SIS epidemic model with unbounded infection force","doi":"10.1016/j.nonrwa.2022.103820","date_updated":"2024-04-07T12:43:53Z","publisher":"Elsevier BV","date_created":"2024-04-07T12:43:49Z","author":[{"full_name":"Tao, Youshan","last_name":"Tao","first_name":"Youshan"},{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"volume":71,"year":"2023","citation":{"ama":"Tao Y, Winkler M. Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. <i>Nonlinear Analysis: Real World Applications</i>. 2023;71. doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">10.1016/j.nonrwa.2022.103820</a>","ieee":"Y. Tao and M. Winkler, “Analysis of a chemotaxis-SIS epidemic model with unbounded infection force,” <i>Nonlinear Analysis: Real World Applications</i>, vol. 71, Art. no. 103820, 2023, doi: <a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">10.1016/j.nonrwa.2022.103820</a>.","chicago":"Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” <i>Nonlinear Analysis: Real World Applications</i> 71 (2023). <a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">https://doi.org/10.1016/j.nonrwa.2022.103820</a>.","apa":"Tao, Y., &#38; Winkler, M. (2023). Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. <i>Nonlinear Analysis: Real World Applications</i>, <i>71</i>, Article 103820. <a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">https://doi.org/10.1016/j.nonrwa.2022.103820</a>","mla":"Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” <i>Nonlinear Analysis: Real World Applications</i>, vol. 71, 103820, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">10.1016/j.nonrwa.2022.103820</a>.","short":"Y. Tao, M. Winkler, Nonlinear Analysis: Real World Applications 71 (2023).","bibtex":"@article{Tao_Winkler_2023, title={Analysis of a chemotaxis-SIS epidemic model with unbounded infection force}, volume={71}, DOI={<a href=\"https://doi.org/10.1016/j.nonrwa.2022.103820\">10.1016/j.nonrwa.2022.103820</a>}, number={103820}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Tao, Youshan and Winkler, Michael}, year={2023} }"},"intvolume":"        71","publication_status":"published","publication_identifier":{"issn":["1468-1218"]},"article_number":"103820","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"language":[{"iso":"eng"}],"_id":"53329","user_id":"31496","status":"public","type":"journal_article","publication":"Nonlinear Analysis: Real World Applications"},{"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Mathematics"],"user_id":"31496","_id":"53326","status":"public","type":"journal_article","publication":"Communications in Mathematical Sciences","doi":"10.4310/cms.2023.v21.n2.a1","title":"Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities","date_created":"2024-04-07T12:41:49Z","author":[{"full_name":"Li, Genglin","last_name":"Li","first_name":"Genglin"},{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"volume":21,"publisher":"International Press of Boston","date_updated":"2024-04-07T12:41:54Z","citation":{"ieee":"G. Li and M. Winkler, “Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities,” <i>Communications in Mathematical Sciences</i>, vol. 21, no. 2, pp. 299–322, 2023, doi: <a href=\"https://doi.org/10.4310/cms.2023.v21.n2.a1\">10.4310/cms.2023.v21.n2.a1</a>.","chicago":"Li, Genglin, and Michael Winkler. “Relaxation in a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” <i>Communications in Mathematical Sciences</i> 21, no. 2 (2023): 299–322. <a href=\"https://doi.org/10.4310/cms.2023.v21.n2.a1\">https://doi.org/10.4310/cms.2023.v21.n2.a1</a>.","ama":"Li G, Winkler M. Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. <i>Communications in Mathematical Sciences</i>. 2023;21(2):299-322. doi:<a href=\"https://doi.org/10.4310/cms.2023.v21.n2.a1\">10.4310/cms.2023.v21.n2.a1</a>","mla":"Li, Genglin, and Michael Winkler. “Relaxation in a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” <i>Communications in Mathematical Sciences</i>, vol. 21, no. 2, International Press of Boston, 2023, pp. 299–322, doi:<a href=\"https://doi.org/10.4310/cms.2023.v21.n2.a1\">10.4310/cms.2023.v21.n2.a1</a>.","short":"G. Li, M. Winkler, Communications in Mathematical Sciences 21 (2023) 299–322.","bibtex":"@article{Li_Winkler_2023, title={Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities}, volume={21}, DOI={<a href=\"https://doi.org/10.4310/cms.2023.v21.n2.a1\">10.4310/cms.2023.v21.n2.a1</a>}, number={2}, journal={Communications in Mathematical Sciences}, publisher={International Press of Boston}, author={Li, Genglin and Winkler, Michael}, year={2023}, pages={299–322} }","apa":"Li, G., &#38; Winkler, M. (2023). Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. <i>Communications in Mathematical Sciences</i>, <i>21</i>(2), 299–322. <a href=\"https://doi.org/10.4310/cms.2023.v21.n2.a1\">https://doi.org/10.4310/cms.2023.v21.n2.a1</a>"},"page":"299-322","intvolume":"        21","year":"2023","issue":"2","publication_status":"published","publication_identifier":{"issn":["1539-6746","1945-0796"]}}]