[{"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Analysis"],"user_id":"31496","_id":"53318","status":"public","type":"journal_article","publication":"Applicable Analysis","doi":"10.1080/00036811.2023.2173183","title":"Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities","date_created":"2024-04-07T12:32:55Z","author":[{"first_name":"Genglin","full_name":"Li, Genglin","last_name":"Li"},{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"volume":103,"date_updated":"2024-04-07T12:36:11Z","publisher":"Informa UK Limited","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","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.","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","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.","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} }"},"page":"45-64","intvolume":" 103","year":"2023","issue":"1","publication_status":"published","publication_identifier":{"issn":["0003-6811","1563-504X"]}},{"user_id":"31496","_id":"53328","status":"public","type":"journal_article","doi":"10.1142/s0218202523500045","volume":33,"author":[{"first_name":"Youshan","last_name":"Tao","full_name":"Tao, Youshan"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"date_updated":"2024-04-07T12:43:17Z","page":"103-138","intvolume":" 33","citation":{"apa":"Tao, Y., & Winkler, M. (2023). Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Mathematical Models and Methods in Applied Sciences, 33(01), 103–138. https://doi.org/10.1142/s0218202523500045","mla":"Tao, Youshan, and Michael Winkler. “Small-Signal Solutions to a Nonlocal Cross-Diffusion Model for Interaction of Scroungers with Rapidly Diffusing Foragers.” Mathematical Models and Methods in Applied Sciences, vol. 33, no. 01, World Scientific Pub Co Pte Ltd, 2023, pp. 103–38, doi:10.1142/s0218202523500045.","short":"Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 33 (2023) 103–138.","bibtex":"@article{Tao_Winkler_2023, title={Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers}, volume={33}, DOI={10.1142/s0218202523500045}, number={01}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Tao, Youshan and Winkler, Michael}, year={2023}, pages={103–138} }","ama":"Tao Y, Winkler M. Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Mathematical Models and Methods in Applied Sciences. 2023;33(01):103-138. doi:10.1142/s0218202523500045","ieee":"Y. Tao and M. Winkler, “Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers,” Mathematical Models and Methods in Applied Sciences, vol. 33, no. 01, pp. 103–138, 2023, doi: 10.1142/s0218202523500045.","chicago":"Tao, Youshan, and Michael Winkler. “Small-Signal Solutions to a Nonlocal Cross-Diffusion Model for Interaction of Scroungers with Rapidly Diffusing Foragers.” Mathematical Models and Methods in Applied Sciences 33, no. 01 (2023): 103–38. https://doi.org/10.1142/s0218202523500045."},"publication_identifier":{"issn":["0218-2025","1793-6314"]},"publication_status":"published","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Modeling and Simulation"],"abstract":[{"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. ","lang":"eng"}],"publication":"Mathematical Models and Methods in Applied Sciences","title":"Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers","date_created":"2024-04-07T12:43:13Z","publisher":"World Scientific Pub Co Pte Ltd","year":"2023","issue":"01"},{"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","volume":62,"author":[{"first_name":"Jaewook","full_name":"Ahn, Jaewook","last_name":"Ahn"},{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2024-04-07T12:40:02Z","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.","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"},"publication_identifier":{"issn":["0944-2669","1432-0835"]},"publication_status":"published","issue":"6","keyword":["Applied Mathematics","Analysis"],"article_number":"180","language":[{"iso":"eng"}],"_id":"53324","user_id":"31496","status":"public","publication":"Calculus of Variations and Partial Differential Equations","type":"journal_article"},{"language":[{"iso":"eng"}],"article_number":"103820","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"user_id":"31496","_id":"53329","status":"public","type":"journal_article","publication":"Nonlinear Analysis: Real World Applications","doi":"10.1016/j.nonrwa.2022.103820","title":"Analysis of a chemotaxis-SIS epidemic model with unbounded infection force","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,"date_updated":"2024-04-07T12:43:53Z","publisher":"Elsevier BV","citation":{"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.","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).","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","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","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."},"intvolume":" 71","year":"2023","publication_status":"published","publication_identifier":{"issn":["1468-1218"]}},{"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Mathematics"],"user_id":"31496","_id":"53326","status":"public","publication":"Communications in Mathematical Sciences","type":"journal_article","doi":"10.4310/cms.2023.v21.n2.a1","title":"Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities","volume":21,"date_created":"2024-04-07T12:41:49Z","author":[{"first_name":"Genglin","last_name":"Li","full_name":"Li, Genglin"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_updated":"2024-04-07T12:41:54Z","publisher":"International Press of Boston","page":"299-322","intvolume":" 21","citation":{"ama":"Li G, Winkler M. Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Communications in Mathematical Sciences. 2023;21(2):299-322. doi:10.4310/cms.2023.v21.n2.a1","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.","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","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.","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} }"},"year":"2023","issue":"2","publication_identifier":{"issn":["1539-6746","1945-0796"]},"publication_status":"published"},{"doi":"10.1515/math-2022-0578","title":"Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2024-04-07T12:54:31Z","volume":21,"publisher":"Walter de Gruyter GmbH","date_updated":"2024-04-07T12:54:34Z","citation":{"ama":"Winkler M. Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. Open Mathematics. 2023;21(1). doi:10.1515/math-2022-0578","ieee":"M. Winkler, “Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type,” Open Mathematics, vol. 21, no. 1, 2023, doi: 10.1515/math-2022-0578.","chicago":"Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” Open Mathematics 21, no. 1 (2023). https://doi.org/10.1515/math-2022-0578.","apa":"Winkler, M. (2023). Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. Open Mathematics, 21(1). https://doi.org/10.1515/math-2022-0578","short":"M. Winkler, Open Mathematics 21 (2023).","mla":"Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” Open Mathematics, vol. 21, no. 1, Walter de Gruyter GmbH, 2023, doi:10.1515/math-2022-0578.","bibtex":"@article{Winkler_2023, title={Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type}, volume={21}, DOI={10.1515/math-2022-0578}, number={1}, journal={Open Mathematics}, publisher={Walter de Gruyter GmbH}, author={Winkler, Michael}, year={2023} }"},"intvolume":" 21","year":"2023","issue":"1","publication_status":"published","publication_identifier":{"issn":["2391-5455"]},"language":[{"iso":"eng"}],"keyword":["General Mathematics"],"user_id":"31496","_id":"53343","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 ."}],"type":"journal_article","publication":"Open Mathematics"},{"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."}],"publication":"Nonlinearity","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Physics and Astronomy","Mathematical Physics","Statistical and Nonlinear Physics"],"user_id":"31496","_id":"53345","page":"4438-4469","intvolume":" 36","citation":{"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.","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.","ama":"Winkler M. Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. Nonlinearity. 2023;36(8):4438-4469. doi:10.1088/1361-6544/ace22e","apa":"Winkler, M. (2023). Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. Nonlinearity, 36(8), 4438–4469. https://doi.org/10.1088/1361-6544/ace22e","short":"M. Winkler, Nonlinearity 36 (2023) 4438–4469.","mla":"Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity, vol. 36, no. 8, IOP Publishing, 2023, pp. 4438–69, doi:10.1088/1361-6544/ace22e.","bibtex":"@article{Winkler_2023, title={Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction}, volume={36}, DOI={10.1088/1361-6544/ace22e}, number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Winkler, Michael}, year={2023}, pages={4438–4469} }"},"year":"2023","issue":"8","publication_identifier":{"issn":["0951-7715","1361-6544"]},"publication_status":"published","doi":"10.1088/1361-6544/ace22e","title":"Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction","volume":36,"date_created":"2024-04-07T12:56:35Z","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"date_updated":"2024-04-07T12:56:40Z","publisher":"IOP Publishing"},{"publication":"Journal of Elliptic and Parabolic Equations","type":"journal_article","abstract":[{"text":"AbstractThe Cauchy problem in $$\\mathbb {R}^n$$\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n is considered for the Keller–Segel system $$\\begin{aligned} \\left\\{ \\begin{array}{l}u_t = \\Delta u - \\nabla \\cdot (u\\nabla v), \\\\ 0 = \\Delta v + u, \\end{array} \\right. \\qquad \\qquad (\\star ) \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n Δ\r\n u\r\n -\r\n ∇\r\n ·\r\n \r\n (\r\n u\r\n ∇\r\n v\r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n +\r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n (\r\n ⋆\r\n )\r\n \r\n \r\n \r\n \r\n \r\n \r\n with a focus on a detailed description of behavior in the presence of nonnegative radially symmetric initial data $$u_0$$\r\n \r\n u\r\n 0\r\n \r\n with non-integrable behavior at spatial infinity. It is shown that if $$u_0$$\r\n \r\n u\r\n 0\r\n \r\n is continuous and bounded, then ($$\\star $$\r\n ⋆\r\n ) admits a local-in-time classical solution, whereas if $$u_0(x)\\rightarrow +\\infty $$\r\n \r\n \r\n u\r\n 0\r\n \r\n \r\n (\r\n x\r\n )\r\n \r\n →\r\n +\r\n ∞\r\n \r\n as $$|x|\\rightarrow \\infty $$\r\n \r\n |\r\n x\r\n |\r\n →\r\n ∞\r\n \r\n , then no such solution can be found. Furthermore, a collection of three sufficient criteria for either global existence or global nonexistence indicates that with respect to the occurrence of finite-time blow-up, spatial decay properties of an explicit singular steady state plays a critical role. In particular, this underlines that explosions in ($$\\star $$\r\n ⋆\r\n ) need not be enforced by initially high concentrations near finite points, but can be exclusively due to large tails.","lang":"eng"}],"status":"public","_id":"53341","user_id":"31496","keyword":["Applied Mathematics","Numerical Analysis","Analysis"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2296-9020","2296-9039"]},"publication_status":"published","issue":"2","year":"2023","intvolume":" 9","page":"919-959","citation":{"ama":"Winkler M. Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity. Journal of Elliptic and Parabolic Equations. 2023;9(2):919-959. doi:10.1007/s41808-023-00230-y","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.","short":"M. Winkler, Journal of Elliptic and Parabolic Equations 9 (2023) 919–959.","bibtex":"@article{Winkler_2023, title={Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity}, volume={9}, DOI={10.1007/s41808-023-00230-y}, number={2}, journal={Journal of Elliptic and Parabolic Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2023}, pages={919–959} }","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.","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"},"date_updated":"2024-04-07T12:52:55Z","publisher":"Springer Science and Business Media LLC","volume":9,"author":[{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2024-04-07T12:52:52Z","title":"Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity","doi":"10.1007/s41808-023-00230-y"},{"doi":"10.1002/mma.9419","title":"Keller–Segel–Stokes interaction involving signal‐dependent motilities","author":[{"last_name":"Tian","full_name":"Tian, Yu","first_name":"Yu"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"date_created":"2024-04-07T12:51:27Z","volume":46,"publisher":"Wiley","date_updated":"2024-04-07T12:51:31Z","citation":{"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.","short":"Y. Tian, M. Winkler, Mathematical Methods in the Applied Sciences 46 (2023) 15667–15683.","bibtex":"@article{Tian_Winkler_2023, title={Keller–Segel–Stokes interaction involving signal‐dependent motilities}, volume={46}, DOI={10.1002/mma.9419}, number={14}, journal={Mathematical Methods in the Applied Sciences}, publisher={Wiley}, author={Tian, Yu and Winkler, Michael}, year={2023}, pages={15667–15683} }","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"},"intvolume":" 46","page":"15667-15683","year":"2023","issue":"14","publication_status":"published","publication_identifier":{"issn":["0170-4214","1099-1476"]},"language":[{"iso":"eng"}],"keyword":["General Engineering","General Mathematics"],"user_id":"31496","_id":"53339","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"},{"status":"public","type":"journal_article","publication":"SIAM Journal on Applied Mathematics","keyword":["Applied Mathematics"],"language":[{"iso":"eng"}],"_id":"53340","user_id":"31496","year":"2023","citation":{"apa":"Painter, K. J., & Winkler, M. (2023). Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. SIAM Journal on Applied Mathematics, 83(5), 2096–2117. https://doi.org/10.1137/22m1539393","bibtex":"@article{Painter_Winkler_2023, title={Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}, volume={83}, DOI={10.1137/22m1539393}, number={5}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Painter, Kevin J. and Winkler, Michael}, year={2023}, pages={2096–2117} }","short":"K.J. Painter, M. Winkler, SIAM Journal on Applied Mathematics 83 (2023) 2096–2117.","mla":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” SIAM Journal on Applied Mathematics, vol. 83, no. 5, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 2096–117, doi:10.1137/22m1539393.","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.","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"},"page":"2096-2117","intvolume":" 83","publication_status":"published","publication_identifier":{"issn":["0036-1399","1095-712X"]},"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":"2024-04-07T12:52:06Z","author":[{"first_name":"Kevin J.","last_name":"Painter","full_name":"Painter, Kevin J."},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"date_created":"2024-04-07T12:52:03Z","volume":83},{"type":"journal_article","publication":"Journal of Differential Equations","status":"public","user_id":"31496","_id":"53342","language":[{"iso":"eng"}],"keyword":["Analysis","Applied Mathematics"],"publication_status":"published","publication_identifier":{"issn":["0022-0396"]},"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","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.","apa":"Winkler, M., & Yokota, T. (2023). Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems. Journal of Differential Equations, 374, 1–28. https://doi.org/10.1016/j.jde.2023.07.029","mla":"Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena by Arbitrarily Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes Systems.” Journal of Differential Equations, vol. 374, Elsevier BV, 2023, pp. 1–28, doi:10.1016/j.jde.2023.07.029.","short":"M. Winkler, T. Yokota, Journal of Differential Equations 374 (2023) 1–28.","bibtex":"@article{Winkler_Yokota_2023, title={Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems}, volume={374}, DOI={10.1016/j.jde.2023.07.029}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler, Michael and Yokota, Tomomi}, year={2023}, pages={1–28} }"},"page":"1-28","intvolume":" 374","year":"2023","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"},{"full_name":"Yokota, Tomomi","last_name":"Yokota","first_name":"Tomomi"}],"date_created":"2024-04-07T12:53:32Z","volume":374,"publisher":"Elsevier BV","date_updated":"2024-04-07T12:53:38Z","doi":"10.1016/j.jde.2023.07.029","title":"Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems"},{"status":"public","publication":"Advances in Differential Equations","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Analysis"],"user_id":"31496","_id":"53346","intvolume":" 28","citation":{"ama":"Winkler M. 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Berlin/Boston: De Gruyter, 2023. https://doi.org/10.1515/9783110745504."},"place":"Berlin/Boston","year":"2023","publication_status":"published","doi":"https://doi.org/10.1515/9783110745504","title":"CLIL - Content and Language Integrated Learning","date_created":"2023-01-10T23:28:10Z","author":[{"id":"65153","full_name":"Böttger, Lydia","last_name":"Böttger","first_name":"Lydia"},{"first_name":"Constanze","id":"54999","full_name":"Niederhaus, Constanze","last_name":"Niederhaus"}],"publisher":"De Gruyter","date_updated":"2024-04-10T14:59:38Z","status":"public","editor":[{"first_name":"Christian","full_name":"Efing, Christian","last_name":"Efing"},{"full_name":"Kalkavan-Aydin, Zeynep","last_name":"Kalkavan-Aydin","first_name":"Zeynep"}],"publication":"Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive","type":"book_chapter","language":[{"iso":"ger"}],"department":[{"_id":"5"}],"user_id":"65153","_id":"35904"},{"date_created":"2024-04-10T13:45:59Z","author":[{"last_name":"Wolf","full_name":"Wolf, Lasse L.","first_name":"Lasse L."},{"first_name":"Hong-Wei","full_name":"Zhang, Hong-Wei","last_name":"Zhang"}],"date_updated":"2024-04-10T13:48:17Z","title":"$L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces","citation":{"ama":"Wolf LL, Zhang H-W. $L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces. arXiv:231111770. Published online 2023.","ieee":"L. L. Wolf and H.-W. Zhang, “$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces,” arXiv:2311.11770. 2023.","chicago":"Wolf, Lasse L., and Hong-Wei Zhang. “$L^2$-Spectrum, Growth Indicator Function and Critical Exponent on  Locally Symmetric Spaces.” ArXiv:2311.11770, 2023.","apa":"Wolf, L. L., & Zhang, H.-W. (2023). $L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces. In arXiv:2311.11770.","bibtex":"@article{Wolf_Zhang_2023, title={$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces}, journal={arXiv:2311.11770}, author={Wolf, Lasse L. and Zhang, Hong-Wei}, year={2023} }","mla":"Wolf, Lasse L., and Hong-Wei Zhang. “$L^2$-Spectrum, Growth Indicator Function and Critical Exponent on  Locally Symmetric Spaces.” ArXiv:2311.11770, 2023.","short":"L.L. Wolf, H.-W. Zhang, ArXiv:2311.11770 (2023)."},"year":"2023","department":[{"_id":"10"},{"_id":"548"}],"user_id":"45027","external_id":{"arxiv":["2311.11770"]},"_id":"53404","language":[{"iso":"eng"}],"publication":"arXiv:2311.11770","type":"preprint","status":"public","abstract":[{"lang":"eng","text":"In this short note we observe, on locally symmetric spaces of higher rank, a\r\nconnection between the growth indicator function introduced by Quint and the\r\nmodified critical exponent of the Poincar\\'e series equipped with the\r\npolyhedral distance. As a consequence, we provide a different characterization\r\nof the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms\r\nof the growth indicator function. Moreover, we explore the relationship between\r\nthese three objects and the temperedness."}]},{"main_file_link":[{"url":"https://www.bibb.de/dienst/publikationen/de/download/18616"}],"title":"Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis","author":[{"last_name":"Jenert","orcid":" https://orcid.org/0000-0001-9262-5646","id":"71994","full_name":"Jenert, Tobias","first_name":"Tobias"}],"date_created":"2024-04-11T06:29:37Z","publisher":"Bundesinstitut für Berufsbildung.","date_updated":"2024-04-11T06:30:05Z","page":"11-24","citation":{"ama":"Jenert T. Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis. In: Kremer H-H, Ertl H, Sloane PFE, eds. Wissenschaft Trifft Praxis – Designbasierte Forschung in Der Beruflichen Bildung. Bundesinstitut für Berufsbildung.; 2023:11-24.","chicago":"Jenert, Tobias. “Design-Based Research Als Erforschung Und Gestaltung von Interaktionsprozessen Zwischen Wissenschaft Und Bildungspraxis.” In Wissenschaft Trifft Praxis – Designbasierte Forschung in Der Beruflichen Bildung, edited by H.-Hugo Kremer, Hubert Ertl, and Peter F. E. Sloane, 11–24. Bonn: Bundesinstitut für Berufsbildung., 2023.","ieee":"T. Jenert, “Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis,” in Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung, H.-H. Kremer, H. Ertl, and P. F. E. Sloane, Eds. Bonn: Bundesinstitut für Berufsbildung., 2023, pp. 11–24.","mla":"Jenert, Tobias. “Design-Based Research Als Erforschung Und Gestaltung von Interaktionsprozessen Zwischen Wissenschaft Und Bildungspraxis.” Wissenschaft Trifft Praxis – Designbasierte Forschung in Der Beruflichen Bildung, edited by H.-Hugo Kremer et al., Bundesinstitut für Berufsbildung., 2023, pp. 11–24.","short":"T. Jenert, in: H.-H. Kremer, H. Ertl, P.F.E. Sloane (Eds.), Wissenschaft Trifft Praxis – Designbasierte Forschung in Der Beruflichen Bildung, Bundesinstitut für Berufsbildung., Bonn, 2023, pp. 11–24.","bibtex":"@inbook{Jenert_2023, place={Bonn}, title={Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis}, booktitle={Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung}, publisher={Bundesinstitut für Berufsbildung.}, author={Jenert, Tobias}, editor={Kremer, H.-Hugo and Ertl, Hubert and Sloane, Peter F. E.}, year={2023}, pages={11–24} }","apa":"Jenert, T. (2023). Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis. In H.-H. Kremer, H. Ertl, & P. F. E. Sloane (Eds.), Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung (pp. 11–24). Bundesinstitut für Berufsbildung."},"place":"Bonn","year":"2023","quality_controlled":"1","language":[{"iso":"eng"}],"department":[{"_id":"208"}],"user_id":"71994","_id":"53405","status":"public","editor":[{"last_name":"Kremer","full_name":"Kremer, H.-Hugo","first_name":"H.-Hugo"},{"full_name":"Ertl, Hubert","last_name":"Ertl","first_name":"Hubert"},{"last_name":"Sloane","full_name":"Sloane, Peter F. E.","first_name":"Peter F. E."}],"abstract":[{"text":"Das Verhältnis zwischen Wissenschaft und Praxis wurde in unterschiedlichen Forschungsansätzen im-\r\nmer wieder wissenschaftlich betrachtet. Dennoch ist es notwendig, sich im Rahmen der wissenschafts-\r\ntheoretischen Konzeption von Design-Based Research (DBR) weiter damit auseinanderzusetzen, denn\r\nInteraktion zwischen Wissenschaft und Bildungspraxis ist ein zentrales Merkmal von DBR. Dieser Beitrag\r\nbefasst sich mit der Frage, wie sich diese Interaktion je nach zugrunde liegendem DBR-Verständnis me-\r\nthodologisch fassen lässt. Die Interaktion wird als ein wesentlicher Bestandteil des Erkenntnisprozesses\r\nin DBR aufgefasst. Daher wird neben der methodischen Ausgestaltung von Interaktionsprozessen auch\r\nmethodologisch reflektiert, was die Wissenschaft-Praxis-Interaktion für die Erkenntnis an sich bedeutet.","lang":"eng"}],"publication":"Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung","type":"book_chapter"},{"language":[{"iso":"eng"}],"_id":"52380","user_id":"58465","department":[{"_id":"67"}],"status":"public","type":"conference","publication":"Proceedings of the 23rd Koli Calling International Conference on Computing Education Research","title":"JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks","doi":"10.1145/3631802.3631824","publisher":"ACM","date_updated":"2024-04-11T12:30:59Z","author":[{"full_name":"Sparmann, Sören","id":"63216","last_name":"Sparmann","first_name":"Sören"},{"first_name":"Sven","last_name":"Hüsing","id":"58465","full_name":"Hüsing, Sven"},{"first_name":"Carsten","full_name":"Schulte, Carsten","id":"60311","last_name":"Schulte"}],"date_created":"2024-03-08T08:02:10Z","year":"2023","citation":{"apa":"Sparmann, S., Hüsing, S., & Schulte, C. (2023). JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks. Proceedings of the 23rd Koli Calling International Conference on Computing Education Research. https://doi.org/10.1145/3631802.3631824","bibtex":"@inproceedings{Sparmann_Hüsing_Schulte_2023, title={JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks}, DOI={10.1145/3631802.3631824}, booktitle={Proceedings of the 23rd Koli Calling International Conference on Computing Education Research}, publisher={ACM}, author={Sparmann, Sören and Hüsing, Sven and Schulte, Carsten}, year={2023} }","short":"S. Sparmann, S. Hüsing, C. Schulte, in: Proceedings of the 23rd Koli Calling International Conference on Computing Education Research, ACM, 2023.","mla":"Sparmann, Sören, et al. “JuGaze: A Cell-Based Eye Tracking and Logging Tool for Jupyter Notebooks.” Proceedings of the 23rd Koli Calling International Conference on Computing Education Research, ACM, 2023, doi:10.1145/3631802.3631824.","ama":"Sparmann S, Hüsing S, Schulte C. JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks. In: Proceedings of the 23rd Koli Calling International Conference on Computing Education Research. ACM; 2023. doi:10.1145/3631802.3631824","ieee":"S. Sparmann, S. Hüsing, and C. Schulte, “JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks,” 2023, doi: 10.1145/3631802.3631824.","chicago":"Sparmann, Sören, Sven Hüsing, and Carsten Schulte. “JuGaze: A Cell-Based Eye Tracking and Logging Tool for Jupyter Notebooks.” In Proceedings of the 23rd Koli Calling International Conference on Computing Education Research. ACM, 2023. https://doi.org/10.1145/3631802.3631824."},"publication_status":"published"}]