[{"user_id":"31496","_id":"63288","language":[{"iso":"eng"}],"article_number":"20220578","type":"journal_article","publication":"Open Mathematics","status":"public","abstract":[{"text":"Abstract\r\n The Cauchy problem in \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n {{\\mathbb{R}}}^{n}\r\n \r\n , \r\n \r\n \r\n \r\n n\r\n ≥\r\n 2\r\n \r\n n\\ge 2\r\n \r\n , for \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n \r\n \r\n t\r\n \r\n \r\n =\r\n Δ\r\n u\r\n −\r\n \r\n ∇\r\n \r\n ⋅\r\n \r\n (\r\n \r\n u\r\n S\r\n ⋅\r\n \r\n ∇\r\n \r\n v\r\n \r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n +\r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n (\r\n \r\n ⋆\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n \\begin{array}{r}\\left\\{\\phantom{\\rule[-1.25em]{}{0ex}}\\begin{array}{l}{u}_{t}=\\Delta u-\\nabla \\cdot \\left(uS\\cdot \\nabla v),\\\\ 0=\\Delta v+u,\\end{array}\\right.\\hspace{2.0em}\\hspace{2.0em}\\hspace{2.0em}\\left(\\star )\\end{array}\r\n \r\n is considered for general matrices \r\n \r\n \r\n \r\n S\r\n ∈\r\n \r\n \r\n R\r\n \r\n \r\n n\r\n ×\r\n n\r\n \r\n \r\n \r\n S\\in {{\\mathbb{R}}}^{n\\times n}\r\n \r\n . A theory of local-in-time classical existence and extensibility is developed in a framework that differs from those considered in large parts of the literature by involving bounded classical solutions. Specifically, it is shown that for all non-negative initial data belonging to \r\n \r\n \r\n \r\n BUC\r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n ∩\r\n \r\n \r\n L\r\n \r\n \r\n p\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n {\\rm{BUC}}\\left({{\\mathbb{R}}}^{n})\\cap {L}^{p}\\left({{\\mathbb{R}}}^{n})\r\n \r\n with some \r\n \r\n \r\n \r\n p\r\n ∈\r\n \r\n [\r\n \r\n 1\r\n ,\r\n n\r\n \r\n )\r\n \r\n \r\n p\\in \\left[1,n)\r\n \r\n , there exist \r\n \r\n \r\n \r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n ∈\r\n \r\n (\r\n \r\n 0\r\n ,\r\n ∞\r\n \r\n ]\r\n \r\n \r\n {T}_{\\max }\\in \\left(0,\\infty ]\r\n \r\n and a uniquely determined \r\n \r\n \r\n \r\n u\r\n ∈\r\n \r\n \r\n C\r\n \r\n \r\n 0\r\n \r\n \r\n \r\n (\r\n \r\n \r\n [\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n ;\r\n \r\n BUC\r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n )\r\n \r\n ∩\r\n \r\n \r\n C\r\n \r\n \r\n 0\r\n \r\n \r\n \r\n (\r\n \r\n \r\n [\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n ;\r\n \r\n \r\n \r\n L\r\n \r\n \r\n p\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n )\r\n \r\n ∩\r\n \r\n \r\n C\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n ×\r\n \r\n (\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n \r\n )\r\n \r\n \r\n u\\in {C}^{0}\\left(\\left[0,{T}_{\\max });\\hspace{0.33em}{\\rm{BUC}}\\left({{\\mathbb{R}}}^{n}))\\cap {C}^{0}\\left(\\left[0,{T}_{\\max });\\hspace{0.33em}{L}^{p}\\left({{\\mathbb{R}}}^{n}))\\cap {C}^{\\infty }\\left({{\\mathbb{R}}}^{n}\\times \\left(0,{T}_{\\max }))\r\n \r\n such that with \r\n \r\n \r\n \r\n v\r\n ≔\r\n Γ\r\n ⋆\r\n u\r\n \r\n v:= \\Gamma \\star u\r\n \r\n , and with \r\n \r\n \r\n \r\n Γ\r\n \r\n \\Gamma \r\n \r\n denoting the Newtonian kernel on \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n {{\\mathbb{R}}}^{n}\r\n \r\n , the pair \r\n \r\n \r\n \r\n \r\n (\r\n \r\n u\r\n ,\r\n v\r\n \r\n )\r\n \r\n \r\n \\left(u,v)\r\n \r\n forms a classical solution of (\r\n \r\n \r\n \r\n ⋆\r\n \r\n \\star \r\n \r\n ) in \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n ×\r\n \r\n (\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n \r\n {{\\mathbb{R}}}^{n}\\times \\left(0,{T}_{\\max })\r\n \r\n , which has the property that \r\n \r\n \r\n \r\n \r\n if\r\n \r\n \r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n <\r\n ∞\r\n ,\r\n \r\n \r\n \r\n then both\r\n \r\n \r\n \r\n \r\n \r\n limsup\r\n \r\n \r\n t\r\n ↗\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n \r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n \r\n ⋅\r\n ,\r\n t\r\n \r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n \r\n L\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n \r\n =\r\n ∞\r\n \r\n \r\n and\r\n \r\n \r\n \r\n \r\n limsup\r\n \r\n \r\n t\r\n ↗\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n \r\n \r\n \r\n ‖\r\n \r\n ∇\r\n \r\n v\r\n \r\n (\r\n \r\n ⋅\r\n ,\r\n t\r\n \r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n \r\n L\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n \r\n =\r\n ∞\r\n .\r\n \r\n \\hspace{0.1em}\\text{if}\\hspace{0.1em}\\hspace{0.33em}{T}_{\\max }\\lt \\infty ,\\hspace{1.0em}\\hspace{0.1em}\\text{then both}\\hspace{0.1em}\\hspace{0.33em}\\mathop{\\mathrm{limsup}}\\limits_{t\\nearrow {T}_{\\max }}\\Vert u\\left(\\cdot ,t){\\Vert }_{{L}^{\\infty }\\left({{\\mathbb{R}}}^{n})}=\\infty \\hspace{1.0em}\\hspace{0.1em}\\text{and}\\hspace{0.1em}\\hspace{1.0em}\\mathop{\\mathrm{limsup}}\\limits_{t\\nearrow {T}_{\\max }}\\Vert \\nabla v\\left(\\cdot ,t){\\Vert }_{{L}^{\\infty }\\left({{\\mathbb{R}}}^{n})}=\\infty .\r\n \r\n An exemplary application of this provides a result on global classical solvability in cases when \r\n \r\n \r\n \r\n ∣\r\n S\r\n +\r\n 1\r\n ∣\r\n \r\n | S+{\\bf{1}}| \r\n \r\n is sufficiently small, where \r\n \r\n \r\n \r\n 1\r\n =\r\n diag\r\n \r\n \r\n (\r\n \r\n 1\r\n ,\r\n \r\n …\r\n \r\n ,\r\n 1\r\n \r\n )\r\n \r\n \r\n {\\bf{1}}={\\rm{diag}}\\hspace{0.33em}\\left(1,\\ldots ,1)\r\n \r\n .","lang":"eng"}],"date_created":"2025-12-18T19:19:35Z","author":[{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"volume":21,"publisher":"Walter de Gruyter GmbH","date_updated":"2025-12-18T20:07:34Z","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":{"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.","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} }","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)."},"intvolume":" 21","year":"2023"},{"doi":"10.1007/s41808-023-00230-y","title":"Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity","volume":9,"date_created":"2025-12-18T19:19:13Z","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"date_updated":"2025-12-18T20:07:25Z","publisher":"Springer Science and Business Media LLC","page":"919-959","intvolume":" 9","citation":{"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} }","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.","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","ieee":"M. Winkler, “Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity,” Journal of Elliptic and Parabolic Equations, vol. 9, no. 2, pp. 919–959, 2023, doi: 10.1007/s41808-023-00230-y.","chicago":"Winkler, Michael. “Solutions to the Keller–Segel System with Non-Integrable Behavior at Spatial Infinity.” Journal of Elliptic and Parabolic Equations 9, no. 2 (2023): 919–59. https://doi.org/10.1007/s41808-023-00230-y."},"year":"2023","issue":"2","publication_identifier":{"issn":["2296-9020","2296-9039"]},"publication_status":"published","language":[{"iso":"eng"}],"user_id":"31496","_id":"63287","status":"public","abstract":[{"text":"AbstractThe Cauchy problem in $$\\mathbb {R}^n$$\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n is considered for the Keller–Segel system $$\\begin{aligned} \\left\\{ \\begin{array}{l}u_t = \\Delta u - \\nabla \\cdot (u\\nabla v), \\\\ 0 = \\Delta v + u, \\end{array} \\right. \\qquad \\qquad (\\star ) \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n Δ\r\n u\r\n -\r\n ∇\r\n ·\r\n \r\n (\r\n u\r\n ∇\r\n v\r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n +\r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n (\r\n ⋆\r\n )\r\n \r\n \r\n \r\n \r\n \r\n \r\n with a focus on a detailed description of behavior in the presence of nonnegative radially symmetric initial data $$u_0$$\r\n \r\n u\r\n 0\r\n \r\n with non-integrable behavior at spatial infinity. It is shown that if $$u_0$$\r\n \r\n u\r\n 0\r\n \r\n is continuous and bounded, then ($$\\star $$\r\n ⋆\r\n ) admits a local-in-time classical solution, whereas if $$u_0(x)\\rightarrow +\\infty $$\r\n \r\n \r\n u\r\n 0\r\n \r\n \r\n (\r\n x\r\n )\r\n \r\n →\r\n +\r\n ∞\r\n \r\n as $$|x|\\rightarrow \\infty $$\r\n \r\n |\r\n x\r\n |\r\n →\r\n ∞\r\n \r\n , then no such solution can be found. Furthermore, a collection of three sufficient criteria for either global existence or global nonexistence indicates that with respect to the occurrence of finite-time blow-up, spatial decay properties of an explicit singular steady state plays a critical role. In particular, this underlines that explosions in ($$\\star $$\r\n ⋆\r\n ) need not be enforced by initially high concentrations near finite points, but can be exclusively due to large tails.","lang":"eng"}],"publication":"Journal of Elliptic and Parabolic Equations","type":"journal_article"},{"type":"journal_article","publication":"Journal of Differential Equations","status":"public","_id":"63289","user_id":"31496","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0022-0396"]},"year":"2023","citation":{"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","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","ieee":"M. Winkler and T. Yokota, “Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems,” Journal of Differential Equations, vol. 374, pp. 1–28, 2023, doi: 10.1016/j.jde.2023.07.029.","chicago":"Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena by Arbitrarily Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes Systems.” Journal of Differential Equations 374 (2023): 1–28. https://doi.org/10.1016/j.jde.2023.07.029."},"intvolume":" 374","page":"1-28","date_updated":"2025-12-18T20:07:42Z","publisher":"Elsevier BV","date_created":"2025-12-18T19:19:57Z","author":[{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"},{"last_name":"Yokota","full_name":"Yokota, Tomomi","first_name":"Tomomi"}],"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"},{"doi":"10.1142/s0218202523500045","title":"Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers","volume":33,"date_created":"2025-12-18T19:12:35Z","author":[{"first_name":"Youshan","last_name":"Tao","full_name":"Tao, Youshan"},{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"publisher":"World Scientific Pub Co Pte Ltd","date_updated":"2025-12-18T20:10:55Z","intvolume":" 33","page":"103-138","citation":{"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.","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","short":"Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 33 (2023) 103–138.","bibtex":"@article{Tao_Winkler_2023, title={Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers}, volume={33}, DOI={10.1142/s0218202523500045}, number={01}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Tao, Youshan and Winkler, Michael}, year={2023}, pages={103–138} }","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.","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"},"year":"2023","issue":"01","publication_identifier":{"issn":["0218-2025","1793-6314"]},"publication_status":"published","language":[{"iso":"eng"}],"user_id":"31496","_id":"63271","status":"public","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. "}],"publication":"Mathematical Models and Methods in Applied Sciences","type":"journal_article"},{"type":"journal_article","publication":"Calculus of Variations and Partial Differential Equations","status":"public","user_id":"31496","_id":"63267","language":[{"iso":"eng"}],"article_number":"180","issue":"6","publication_status":"published","publication_identifier":{"issn":["0944-2669","1432-0835"]},"citation":{"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.","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.","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} }","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."},"intvolume":" 62","year":"2023","date_created":"2025-12-18T19:10:55Z","author":[{"full_name":"Ahn, Jaewook","last_name":"Ahn","first_name":"Jaewook"},{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"volume":62,"date_updated":"2025-12-18T20:10:21Z","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s00526-023-02523-5","title":"A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system"},{"status":"public","publication":"Communications in Mathematical Sciences","type":"journal_article","language":[{"iso":"eng"}],"_id":"63270","user_id":"31496","year":"2023","page":"299-322","intvolume":" 21","citation":{"short":"G. Li, M. Winkler, Communications in Mathematical Sciences 21 (2023) 299–322.","mla":"Li, Genglin, and Michael Winkler. “Relaxation in a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Communications in Mathematical Sciences, vol. 21, no. 2, International Press of Boston, 2023, pp. 299–322, doi:10.4310/cms.2023.v21.n2.a1.","bibtex":"@article{Li_Winkler_2023, title={Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities}, volume={21}, DOI={10.4310/cms.2023.v21.n2.a1}, number={2}, journal={Communications in Mathematical Sciences}, publisher={International Press of Boston}, author={Li, Genglin and Winkler, Michael}, year={2023}, pages={299–322} }","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","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.","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"},"publication_identifier":{"issn":["1539-6746","1945-0796"]},"publication_status":"published","issue":"2","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","volume":21,"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"},{"language":[{"iso":"eng"}],"article_number":"103820","user_id":"31496","_id":"63273","status":"public","publication":"Nonlinear Analysis: Real World Applications","type":"journal_article","doi":"10.1016/j.nonrwa.2022.103820","title":"Analysis of a chemotaxis-SIS epidemic model with unbounded infection force","volume":71,"date_created":"2025-12-18T19:13:40Z","author":[{"first_name":"Youshan","full_name":"Tao, Youshan","last_name":"Tao"},{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_updated":"2025-12-18T20:11:09Z","publisher":"Elsevier BV","intvolume":" 71","citation":{"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={10.1016/j.nonrwa.2022.103820}, number={103820}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Tao, Youshan and Winkler, Michael}, year={2023} }","mla":"Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” Nonlinear Analysis: Real World Applications, vol. 71, 103820, Elsevier BV, 2023, doi:10.1016/j.nonrwa.2022.103820.","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","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.","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"},"year":"2023","publication_identifier":{"issn":["1468-1218"]},"publication_status":"published"},{"author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:17:01Z","volume":36,"date_updated":"2025-12-18T20:12:06Z","publisher":"IOP Publishing","doi":"10.1088/1361-6544/ace22e","title":"Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction","issue":"8","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"citation":{"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} }","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.","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","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."},"page":"4438-4469","intvolume":" 36","year":"2023","user_id":"31496","_id":"63281","language":[{"iso":"eng"}],"type":"journal_article","publication":"Nonlinearity","status":"public","abstract":[{"lang":"eng","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."}]},{"date_updated":"2025-12-18T20:11:29Z","publisher":"Wiley","date_created":"2025-12-18T19:15:06Z","author":[{"last_name":"Tian","full_name":"Tian, Yu","first_name":"Yu"},{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"volume":46,"title":"Keller–Segel–Stokes interaction involving signal‐dependent motilities","doi":"10.1002/mma.9419","publication_status":"published","publication_identifier":{"issn":["0170-4214","1099-1476"]},"issue":"14","year":"2023","citation":{"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.","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.","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","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","_id":"63276","user_id":"31496","language":[{"iso":"eng"}],"type":"journal_article","publication":"Mathematical Methods in the Applied Sciences","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."}],"status":"public"},{"_id":"63275","user_id":"31496","language":[{"iso":"eng"}],"publication":"Evolution Equations and Control Theory","type":"journal_article","status":"public","date_updated":"2025-12-18T20:11:23Z","publisher":"American Institute of Mathematical Sciences (AIMS)","volume":12,"date_created":"2025-12-18T19:14:46Z","author":[{"last_name":"Tao","full_name":"Tao, Youshan","first_name":"Youshan"},{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"title":"Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities","doi":"10.3934/eect.2023031","publication_identifier":{"issn":["2163-2480"]},"publication_status":"published","issue":"6","year":"2023","intvolume":" 12","page":"1676-1687","citation":{"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} }","short":"Y. Tao, M. Winkler, Evolution Equations and Control Theory 12 (2023) 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.","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","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.","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.","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_status":"published","publication_identifier":{"issn":["0036-1399","1095-712X"]},"issue":"5","year":"2023","citation":{"ieee":"K. J. Painter and M. Winkler, “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities,” SIAM Journal on Applied Mathematics, vol. 83, no. 5, pp. 2096–2117, 2023, doi: 10.1137/22m1539393.","chicago":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” SIAM Journal on Applied Mathematics 83, no. 5 (2023): 2096–2117. https://doi.org/10.1137/22m1539393.","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","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.","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} }","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"},"page":"2096-2117","intvolume":" 83","publisher":"Society for Industrial & Applied Mathematics (SIAM)","date_updated":"2025-12-18T20:11:36Z","date_created":"2025-12-18T19:15:29Z","author":[{"last_name":"Painter","full_name":"Painter, Kevin J.","first_name":"Kevin J."},{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"volume":83,"title":"Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities","doi":"10.1137/22m1539393","type":"journal_article","publication":"SIAM Journal on Applied Mathematics","status":"public","_id":"63277","user_id":"31496","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"article_number":"32","user_id":"31496","_id":"63283","status":"public","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"}],"type":"journal_article","publication":"Zeitschrift für angewandte Mathematik und Physik","doi":"10.1007/s00033-022-01925-3","title":"Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"date_created":"2025-12-18T19:17:51Z","volume":74,"date_updated":"2025-12-18T20:12:20Z","publisher":"Springer Science and Business Media LLC","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","short":"M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 74 (2023).","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} }","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.","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.","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"},"intvolume":" 74","year":"2023","issue":"1","publication_status":"published","publication_identifier":{"issn":["0044-2275","1420-9039"]}},{"doi":"10.1080/00036811.2023.2173183","title":"Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities","volume":103,"author":[{"first_name":"Genglin","full_name":"Li, Genglin","last_name":"Li"},{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-18T19:05:34Z","publisher":"Informa UK Limited","date_updated":"2025-12-18T20:14:04Z","page":"45-64","intvolume":" 103","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","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.","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} }","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.” Applicable Analysis, vol. 103, no. 1, Informa UK Limited, 2023, pp. 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"},"year":"2023","issue":"1","publication_identifier":{"issn":["0003-6811","1563-504X"]},"publication_status":"published","language":[{"iso":"eng"}],"user_id":"31496","_id":"63255","status":"public","publication":"Applicable Analysis","type":"journal_article"},{"language":[{"iso":"eng"}],"_id":"63261","user_id":"31496","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 "}],"status":"public","type":"journal_article","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","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","publisher":"European Mathematical Society - EMS - Publishing House GmbH","date_updated":"2025-12-18T20:14:52Z","author":[{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2025-12-18T19:08:10Z","volume":41,"year":"2023","citation":{"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.","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","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 41 (2023) 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.","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} }"},"intvolume":" 41","page":"95-127","publication_status":"published","publication_identifier":{"issn":["0294-1449","1873-1430"]},"issue":"1"},{"type":"journal_article","status":"public","_id":"53338","user_id":"31496","publication_identifier":{"issn":["0022-2526","1467-9590"]},"publication_status":"published","intvolume":" 151","page":"1197-1229","citation":{"ama":"Lankeit J, Winkler M. Depleting the signal: Analysis of chemotaxis‐consumption models—A survey. Studies in Applied Mathematics. 2023;151(4):1197-1229. doi:10.1111/sapm.12625","ieee":"J. Lankeit and M. Winkler, “Depleting the signal: Analysis of chemotaxis‐consumption models—A survey,” Studies in Applied Mathematics, vol. 151, no. 4, pp. 1197–1229, 2023, doi: 10.1111/sapm.12625.","chicago":"Lankeit, Johannes, and Michael Winkler. “Depleting the Signal: Analysis of Chemotaxis‐consumption Models—A Survey.” Studies in Applied Mathematics 151, no. 4 (2023): 1197–1229. https://doi.org/10.1111/sapm.12625.","bibtex":"@article{Lankeit_Winkler_2023, title={Depleting the signal: Analysis of chemotaxis‐consumption models—A survey}, volume={151}, DOI={10.1111/sapm.12625}, number={4}, journal={Studies in Applied Mathematics}, publisher={Wiley}, author={Lankeit, Johannes and Winkler, Michael}, year={2023}, pages={1197–1229} }","short":"J. Lankeit, M. Winkler, Studies in Applied Mathematics 151 (2023) 1197–1229.","mla":"Lankeit, Johannes, and Michael Winkler. “Depleting the Signal: Analysis of Chemotaxis‐consumption Models—A Survey.” Studies in Applied Mathematics, vol. 151, no. 4, Wiley, 2023, pp. 1197–229, doi:10.1111/sapm.12625.","apa":"Lankeit, J., & Winkler, M. (2023). Depleting the signal: Analysis of chemotaxis‐consumption models—A survey. Studies in Applied Mathematics, 151(4), 1197–1229. https://doi.org/10.1111/sapm.12625"},"date_updated":"2025-12-18T20:16:04Z","volume":151,"author":[{"full_name":"Lankeit, Johannes","last_name":"Lankeit","first_name":"Johannes"},{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"doi":"10.1111/sapm.12625","publication":"Studies in Applied Mathematics","abstract":[{"text":"AbstractWe give an overview of analytical results concerned with chemotaxis systems where the signal is absorbed. We recall results on existence and properties of solutions for the prototypical chemotaxis‐consumption model and various variants and review more recent findings on its ability to support the emergence of spatial structures.","lang":"eng"}],"keyword":["Applied Mathematics"],"language":[{"iso":"eng"}],"issue":"4","year":"2023","publisher":"Wiley","date_created":"2024-04-07T12:50:45Z","title":"Depleting the signal: Analysis of chemotaxis‐consumption models—A survey"},{"year":"2023","citation":{"ama":"Colasuonno F, Winkler M. Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\\R^n$. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. Published online 2023. doi:10.2422/2036-2145.202303_006","chicago":"Colasuonno, Francesca, and Michael Winkler. “Stability vs.~instability of Singular Steady States in the Parabolic-Elliptic Keller-Segel System on $\\R^n$.” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2023. https://doi.org/10.2422/2036-2145.202303_006.","ieee":"F. Colasuonno and M. Winkler, “Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\\R^n$,” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, Art. no. 286, 2023, doi: 10.2422/2036-2145.202303_006.","apa":"Colasuonno, F., & Winkler, M. (2023). Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\\R^n$. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, Article 286. https://doi.org/10.2422/2036-2145.202303_006","mla":"Colasuonno, Francesca, and Michael Winkler. “Stability vs.~instability of Singular Steady States in the Parabolic-Elliptic Keller-Segel System on $\\R^n$.” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 286, Scuola Normale Superiore - Edizioni della Normale, 2023, doi:10.2422/2036-2145.202303_006.","bibtex":"@article{Colasuonno_Winkler_2023, title={Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\\R^n$}, DOI={10.2422/2036-2145.202303_006}, number={286}, journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}, publisher={Scuola Normale Superiore - Edizioni della Normale}, author={Colasuonno, Francesca and Winkler, Michael}, year={2023} }","short":"F. Colasuonno, M. Winkler, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (2023)."},"publication_status":"published","publication_identifier":{"issn":["2036-2145","0391-173X"]},"title":"Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\\R^n$","doi":"10.2422/2036-2145.202303_006","publisher":"Scuola Normale Superiore - Edizioni della Normale","date_updated":"2025-12-18T20:17:21Z","author":[{"first_name":"Francesca","last_name":"Colasuonno","full_name":"Colasuonno, Francesca"},{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-18T18:58:40Z","status":"public","type":"journal_article","publication":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","article_number":"286","language":[{"iso":"eng"}],"_id":"63243","user_id":"31496"},{"status":"public","publication":"IEEE Transactions on Power Electronics","type":"journal_article","keyword":["Electrical and Electronic Engineering"],"language":[{"iso":"eng"}],"_id":"46863","department":[{"_id":"52"}],"user_id":"93461","year":"2023","page":"1-16","citation":{"ama":"Schenke M, Haucke-Korber B, Wallscheid O. Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor. IEEE Transactions on Power Electronics. Published online 2023:1-16. doi:10.1109/tpel.2023.3303651","ieee":"M. Schenke, B. Haucke-Korber, and O. Wallscheid, “Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor,” IEEE Transactions on Power Electronics, pp. 1–16, 2023, doi: 10.1109/tpel.2023.3303651.","chicago":"Schenke, Maximilian, Barnabas Haucke-Korber, and Oliver Wallscheid. “Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor.” IEEE Transactions on Power Electronics, 2023, 1–16. https://doi.org/10.1109/tpel.2023.3303651.","mla":"Schenke, Maximilian, et al. “Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor.” IEEE Transactions on Power Electronics, Institute of Electrical and Electronics Engineers (IEEE), 2023, pp. 1–16, doi:10.1109/tpel.2023.3303651.","bibtex":"@article{Schenke_Haucke-Korber_Wallscheid_2023, title={Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor}, DOI={10.1109/tpel.2023.3303651}, journal={IEEE Transactions on Power Electronics}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Schenke, Maximilian and Haucke-Korber, Barnabas and Wallscheid, Oliver}, year={2023}, pages={1–16} }","short":"M. Schenke, B. Haucke-Korber, O. Wallscheid, IEEE Transactions on Power Electronics (2023) 1–16.","apa":"Schenke, M., Haucke-Korber, B., & Wallscheid, O. (2023). Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor. IEEE Transactions on Power Electronics, 1–16. https://doi.org/10.1109/tpel.2023.3303651"},"publication_identifier":{"issn":["0885-8993","1941-0107"]},"publication_status":"published","title":"Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor","doi":"10.1109/tpel.2023.3303651","date_updated":"2025-12-19T12:44:23Z","publisher":"Institute of Electrical and Electronics Engineers (IEEE)","author":[{"first_name":"Maximilian","last_name":"Schenke","orcid":"0000-0001-5427-9527","id":"52638","full_name":"Schenke, Maximilian"},{"id":"93461","full_name":"Haucke-Korber, Barnabas","orcid":"0000-0003-0862-2069","last_name":"Haucke-Korber","first_name":"Barnabas"},{"full_name":"Wallscheid, Oliver","id":"11291","orcid":"https://orcid.org/0000-0001-9362-8777","last_name":"Wallscheid","first_name":"Oliver"}],"date_created":"2023-09-07T12:08:05Z"},{"publication_status":"published","year":"2023","citation":{"chicago":"Haucke-Korber, Barnabas, Maximilian Schenke, and Oliver Wallscheid. “Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors.” In 2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC). IEEE, 2023. https://doi.org/10.1109/iemdc55163.2023.10239018.","ieee":"B. Haucke-Korber, M. Schenke, and O. Wallscheid, “Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors,” 2023, doi: 10.1109/iemdc55163.2023.10239018.","ama":"Haucke-Korber B, Schenke M, Wallscheid O. Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors. In: 2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC). IEEE; 2023. doi:10.1109/iemdc55163.2023.10239018","short":"B. Haucke-Korber, M. Schenke, O. Wallscheid, in: 2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC), IEEE, 2023.","mla":"Haucke-Korber, Barnabas, et al. “Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors.” 2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC), IEEE, 2023, doi:10.1109/iemdc55163.2023.10239018.","bibtex":"@inproceedings{Haucke-Korber_Schenke_Wallscheid_2023, title={Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors}, DOI={10.1109/iemdc55163.2023.10239018}, booktitle={2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC)}, publisher={IEEE}, author={Haucke-Korber, Barnabas and Schenke, Maximilian and Wallscheid, Oliver}, year={2023} }","apa":"Haucke-Korber, B., Schenke, M., & Wallscheid, O. (2023). Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors. 2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC). https://doi.org/10.1109/iemdc55163.2023.10239018"},"date_updated":"2025-12-19T12:44:15Z","publisher":"IEEE","author":[{"orcid":"0000-0003-0862-2069","last_name":"Haucke-Korber","full_name":"Haucke-Korber, Barnabas","id":"93461","first_name":"Barnabas"},{"id":"52638","full_name":"Schenke, Maximilian","orcid":"0000-0001-5427-9527","last_name":"Schenke","first_name":"Maximilian"},{"first_name":"Oliver","id":"11291","full_name":"Wallscheid, Oliver","last_name":"Wallscheid","orcid":"https://orcid.org/0000-0001-9362-8777"}],"date_created":"2023-09-07T12:08:35Z","title":"Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors","doi":"10.1109/iemdc55163.2023.10239018","publication":"2023 IEEE International Electric Machines & Drives Conference (IEMDC)","type":"conference","status":"public","_id":"46865","department":[{"_id":"52"}],"user_id":"93461","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"_id":"46864","department":[{"_id":"52"}],"user_id":"93461","status":"public","publication":"2023 IEEE International Electric Machines & Drives Conference (IEMDC)","type":"conference","title":"Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives","doi":"10.1109/iemdc55163.2023.10239044","date_updated":"2025-12-19T12:44:03Z","publisher":"IEEE","author":[{"first_name":"Felix","last_name":"Book","full_name":"Book, Felix"},{"first_name":"Arne","last_name":"Traue","full_name":"Traue, Arne"},{"last_name":"Schenke","orcid":"0000-0001-5427-9527","full_name":"Schenke, Maximilian","id":"52638","first_name":"Maximilian"},{"first_name":"Barnabas","id":"93461","full_name":"Haucke-Korber, Barnabas","last_name":"Haucke-Korber","orcid":"0000-0003-0862-2069"},{"first_name":"Oliver","full_name":"Wallscheid, Oliver","id":"11291","last_name":"Wallscheid","orcid":"https://orcid.org/0000-0001-9362-8777"}],"date_created":"2023-09-07T12:08:25Z","year":"2023","citation":{"ama":"Book F, Traue A, Schenke M, Haucke-Korber B, Wallscheid O. Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives. In: 2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC). IEEE; 2023. doi:10.1109/iemdc55163.2023.10239044","ieee":"F. Book, A. Traue, M. Schenke, B. Haucke-Korber, and O. Wallscheid, “Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives,” 2023, doi: 10.1109/iemdc55163.2023.10239044.","chicago":"Book, Felix, Arne Traue, Maximilian Schenke, Barnabas Haucke-Korber, and Oliver Wallscheid. “Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives.” In 2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC). IEEE, 2023. https://doi.org/10.1109/iemdc55163.2023.10239044.","short":"F. Book, A. Traue, M. Schenke, B. Haucke-Korber, O. Wallscheid, in: 2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC), IEEE, 2023.","bibtex":"@inproceedings{Book_Traue_Schenke_Haucke-Korber_Wallscheid_2023, title={Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives}, DOI={10.1109/iemdc55163.2023.10239044}, booktitle={2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC)}, publisher={IEEE}, author={Book, Felix and Traue, Arne and Schenke, Maximilian and Haucke-Korber, Barnabas and Wallscheid, Oliver}, year={2023} }","mla":"Book, Felix, et al. “Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives.” 2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC), IEEE, 2023, doi:10.1109/iemdc55163.2023.10239044.","apa":"Book, F., Traue, A., Schenke, M., Haucke-Korber, B., & Wallscheid, O. (2023). Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives. 2023 IEEE International Electric Machines &amp; Drives Conference (IEMDC). https://doi.org/10.1109/iemdc55163.2023.10239044"},"publication_status":"published"},{"language":[{"iso":"eng"}],"user_id":"76026","department":[{"_id":"36"},{"_id":"1"},{"_id":"612"}],"_id":"25832","status":"public","type":"journal_article","publication":"International Journal of Bilingual Education and Bilingualism","doi":"10.1080/13670050.2021.1981821","title":"Attention to diversity in German CLIL classrooms: Multi-perspective research on students’ and teachers’ perceptions","author":[{"first_name":"Philipp","full_name":"Siepmann, Philipp","last_name":"Siepmann"},{"first_name":"Dominik","full_name":"Rumlich, Dominik","id":"76026","orcid":"0000-0001-8682-450X","last_name":"Rumlich"},{"first_name":"Frauke","full_name":"Matz, Frauke","last_name":"Matz"},{"full_name":"Römhild, Ricardo","last_name":"Römhild","first_name":"Ricardo"}],"date_created":"2021-10-08T05:54:50Z","volume":26,"date_updated":"2025-12-27T09:06:35Z","citation":{"mla":"Siepmann, Philipp, et al. “Attention to Diversity in German CLIL Classrooms: Multi-Perspective Research on Students’ and Teachers’ Perceptions.” International Journal of Bilingual Education and Bilingualism, vol. 26, no. 9, 2023, pp. 1080–96, doi:10.1080/13670050.2021.1981821.","bibtex":"@article{Siepmann_Rumlich_Matz_Römhild_2023, title={Attention to diversity in German CLIL classrooms: Multi-perspective research on students’ and teachers’ perceptions}, volume={26}, DOI={10.1080/13670050.2021.1981821}, number={9}, journal={International Journal of Bilingual Education and Bilingualism}, author={Siepmann, Philipp and Rumlich, Dominik and Matz, Frauke and Römhild, Ricardo}, year={2023}, pages={1080–1096} }","short":"P. Siepmann, D. Rumlich, F. Matz, R. Römhild, International Journal of Bilingual Education and Bilingualism 26 (2023) 1080–1096.","apa":"Siepmann, P., Rumlich, D., Matz, F., & Römhild, R. (2023). Attention to diversity in German CLIL classrooms: Multi-perspective research on students’ and teachers’ perceptions. International Journal of Bilingual Education and Bilingualism, 26(9), 1080–1096. https://doi.org/10.1080/13670050.2021.1981821","ama":"Siepmann P, Rumlich D, Matz F, Römhild R. Attention to diversity in German CLIL classrooms: Multi-perspective research on students’ and teachers’ perceptions. International Journal of Bilingual Education and Bilingualism. 2023;26(9):1080-1096. doi:10.1080/13670050.2021.1981821","ieee":"P. Siepmann, D. Rumlich, F. Matz, and R. Römhild, “Attention to diversity in German CLIL classrooms: Multi-perspective research on students’ and teachers’ perceptions,” International Journal of Bilingual Education and Bilingualism, vol. 26, no. 9, pp. 1080–1096, 2023, doi: 10.1080/13670050.2021.1981821.","chicago":"Siepmann, Philipp, Dominik Rumlich, Frauke Matz, and Ricardo Römhild. “Attention to Diversity in German CLIL Classrooms: Multi-Perspective Research on Students’ and Teachers’ Perceptions.” International Journal of Bilingual Education and Bilingualism 26, no. 9 (2023): 1080–96. https://doi.org/10.1080/13670050.2021.1981821."},"page":"1080-1096","intvolume":" 26","year":"2023","issue":"9"}]