--- _id: '53328' abstract: - lang: eng text: As a simplified version of a three-component taxis cascade model accounting for different migration strategies of two population groups in search of food, a two-component nonlocal nutrient taxis system is considered in a two-dimensional bounded convex domain with smooth boundary. For any given conveniently regular and biologically meaningful initial data, smallness conditions on the prescribed resource growth and on the initial nutrient signal concentration are identified which ensure the global existence of a global classical solution to the corresponding no-flux initial-boundary value problem. Moreover, under additional assumptions on the food production source these solutions are shown to be bounded, and to stabilize toward semi-trivial equilibria in the large time limit, respectively. author: - first_name: Youshan full_name: Tao, Youshan last_name: Tao - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Tao Y, Winkler M. Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Mathematical Models and Methods in Applied Sciences. 2023;33(01):103-138. doi:10.1142/s0218202523500045 apa: Tao, Y., & Winkler, M. (2023). Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Mathematical Models and Methods in Applied Sciences, 33(01), 103–138. https://doi.org/10.1142/s0218202523500045 bibtex: '@article{Tao_Winkler_2023, title={Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers}, volume={33}, DOI={10.1142/s0218202523500045}, number={01}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Tao, Youshan and Winkler, Michael}, year={2023}, pages={103–138} }' chicago: 'Tao, Youshan, and Michael Winkler. “Small-Signal Solutions to a Nonlocal Cross-Diffusion Model for Interaction of Scroungers with Rapidly Diffusing Foragers.” Mathematical Models and Methods in Applied Sciences 33, no. 01 (2023): 103–38. https://doi.org/10.1142/s0218202523500045.' ieee: 'Y. Tao and M. Winkler, “Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers,” Mathematical Models and Methods in Applied Sciences, vol. 33, no. 01, pp. 103–138, 2023, doi: 10.1142/s0218202523500045.' mla: Tao, Youshan, and Michael Winkler. “Small-Signal Solutions to a Nonlocal Cross-Diffusion Model for Interaction of Scroungers with Rapidly Diffusing Foragers.” Mathematical Models and Methods in Applied Sciences, vol. 33, no. 01, World Scientific Pub Co Pte Ltd, 2023, pp. 103–38, doi:10.1142/s0218202523500045. short: Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 33 (2023) 103–138. date_created: 2024-04-07T12:43:13Z date_updated: 2024-04-07T12:43:17Z doi: 10.1142/s0218202523500045 intvolume: ' 33' issue: '01' keyword: - Applied Mathematics - Modeling and Simulation language: - iso: eng page: 103-138 publication: Mathematical Models and Methods in Applied Sciences publication_identifier: issn: - 0218-2025 - 1793-6314 publication_status: published publisher: World Scientific Pub Co Pte Ltd status: public title: Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers type: journal_article user_id: '31496' volume: 33 year: '2023' ... --- _id: '53324' article_number: '180' author: - first_name: Jaewook full_name: Ahn, Jaewook last_name: Ahn - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Ahn J, Winkler M. A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system. Calculus of Variations and Partial Differential Equations. 2023;62(6). doi:10.1007/s00526-023-02523-5 apa: Ahn, J., & Winkler, M. (2023). A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system. Calculus of Variations and Partial Differential Equations, 62(6), Article 180. https://doi.org/10.1007/s00526-023-02523-5 bibtex: '@article{Ahn_Winkler_2023, title={A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system}, volume={62}, DOI={10.1007/s00526-023-02523-5}, number={6180}, journal={Calculus of Variations and Partial Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Ahn, Jaewook and Winkler, Michael}, year={2023} }' chicago: Ahn, Jaewook, and Michael Winkler. “A Critical Exponent for Blow-up in a Two-Dimensional Chemotaxis-Consumption System.” Calculus of Variations and Partial Differential Equations 62, no. 6 (2023). https://doi.org/10.1007/s00526-023-02523-5. ieee: 'J. Ahn and M. Winkler, “A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system,” Calculus of Variations and Partial Differential Equations, vol. 62, no. 6, Art. no. 180, 2023, doi: 10.1007/s00526-023-02523-5.' mla: Ahn, Jaewook, and Michael Winkler. “A Critical Exponent for Blow-up in a Two-Dimensional Chemotaxis-Consumption System.” Calculus of Variations and Partial Differential Equations, vol. 62, no. 6, 180, Springer Science and Business Media LLC, 2023, doi:10.1007/s00526-023-02523-5. short: J. Ahn, M. Winkler, Calculus of Variations and Partial Differential Equations 62 (2023). date_created: 2024-04-07T12:40:02Z date_updated: 2024-04-07T12:40:06Z doi: 10.1007/s00526-023-02523-5 intvolume: ' 62' issue: '6' keyword: - Applied Mathematics - Analysis language: - iso: eng publication: Calculus of Variations and Partial Differential Equations publication_identifier: issn: - 0944-2669 - 1432-0835 publication_status: published publisher: Springer Science and Business Media LLC status: public title: A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system type: journal_article user_id: '31496' volume: 62 year: '2023' ... --- _id: '53329' article_number: '103820' author: - first_name: Youshan full_name: Tao, Youshan last_name: Tao - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: 'Tao Y, Winkler M. Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. Nonlinear Analysis: Real World Applications. 2023;71. doi:10.1016/j.nonrwa.2022.103820' apa: 'Tao, Y., & Winkler, M. (2023). Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. Nonlinear Analysis: Real World Applications, 71, Article 103820. https://doi.org/10.1016/j.nonrwa.2022.103820' bibtex: '@article{Tao_Winkler_2023, title={Analysis of a chemotaxis-SIS epidemic model with unbounded infection force}, volume={71}, DOI={10.1016/j.nonrwa.2022.103820}, number={103820}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Tao, Youshan and Winkler, Michael}, year={2023} }' chicago: 'Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” Nonlinear Analysis: Real World Applications 71 (2023). https://doi.org/10.1016/j.nonrwa.2022.103820.' ieee: 'Y. Tao and M. Winkler, “Analysis of a chemotaxis-SIS epidemic model with unbounded infection force,” Nonlinear Analysis: Real World Applications, vol. 71, Art. no. 103820, 2023, doi: 10.1016/j.nonrwa.2022.103820.' mla: 'Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” Nonlinear Analysis: Real World Applications, vol. 71, 103820, Elsevier BV, 2023, doi:10.1016/j.nonrwa.2022.103820.' short: 'Y. Tao, M. Winkler, Nonlinear Analysis: Real World Applications 71 (2023).' date_created: 2024-04-07T12:43:49Z date_updated: 2024-04-07T12:43:53Z doi: 10.1016/j.nonrwa.2022.103820 intvolume: ' 71' keyword: - Applied Mathematics - Computational Mathematics - General Economics - Econometrics and Finance - General Engineering - General Medicine - Analysis language: - iso: eng publication: 'Nonlinear Analysis: Real World Applications' publication_identifier: issn: - 1468-1218 publication_status: published publisher: Elsevier BV status: public title: Analysis of a chemotaxis-SIS epidemic model with unbounded infection force type: journal_article user_id: '31496' volume: 71 year: '2023' ... --- _id: '53326' author: - first_name: Genglin full_name: Li, Genglin last_name: Li - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Li G, Winkler M. Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Communications in Mathematical Sciences. 2023;21(2):299-322. doi:10.4310/cms.2023.v21.n2.a1 apa: Li, G., & Winkler, M. (2023). Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Communications in Mathematical Sciences, 21(2), 299–322. https://doi.org/10.4310/cms.2023.v21.n2.a1 bibtex: '@article{Li_Winkler_2023, title={Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities}, volume={21}, DOI={10.4310/cms.2023.v21.n2.a1}, number={2}, journal={Communications in Mathematical Sciences}, publisher={International Press of Boston}, author={Li, Genglin and Winkler, Michael}, year={2023}, pages={299–322} }' chicago: 'Li, Genglin, and Michael Winkler. “Relaxation in a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Communications in Mathematical Sciences 21, no. 2 (2023): 299–322. https://doi.org/10.4310/cms.2023.v21.n2.a1.' ieee: 'G. Li and M. Winkler, “Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities,” Communications in Mathematical Sciences, vol. 21, no. 2, pp. 299–322, 2023, doi: 10.4310/cms.2023.v21.n2.a1.' mla: Li, Genglin, and Michael Winkler. “Relaxation in a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Communications in Mathematical Sciences, vol. 21, no. 2, International Press of Boston, 2023, pp. 299–322, doi:10.4310/cms.2023.v21.n2.a1. short: G. Li, M. Winkler, Communications in Mathematical Sciences 21 (2023) 299–322. date_created: 2024-04-07T12:41:49Z date_updated: 2024-04-07T12:41:54Z doi: 10.4310/cms.2023.v21.n2.a1 intvolume: ' 21' issue: '2' keyword: - Applied Mathematics - General Mathematics language: - iso: eng page: 299-322 publication: Communications in Mathematical Sciences publication_identifier: issn: - 1539-6746 - 1945-0796 publication_status: published publisher: International Press of Boston status: public title: Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities type: journal_article user_id: '31496' volume: 21 year: '2023' ... --- _id: '53343' 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 ." author: - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Winkler M. Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. Open Mathematics. 2023;21(1). doi:10.1515/math-2022-0578 apa: Winkler, M. (2023). Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. Open Mathematics, 21(1). 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={1}, journal={Open Mathematics}, publisher={Walter de Gruyter GmbH}, author={Winkler, Michael}, year={2023} }' chicago: Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” Open Mathematics 21, no. 1 (2023). https://doi.org/10.1515/math-2022-0578. ieee: 'M. Winkler, “Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type,” Open Mathematics, vol. 21, no. 1, 2023, doi: 10.1515/math-2022-0578.' mla: Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” Open Mathematics, vol. 21, no. 1, Walter de Gruyter GmbH, 2023, doi:10.1515/math-2022-0578. short: M. Winkler, Open Mathematics 21 (2023). date_created: 2024-04-07T12:54:31Z date_updated: 2024-04-07T12:54:34Z doi: 10.1515/math-2022-0578 intvolume: ' 21' issue: '1' keyword: - General Mathematics language: - iso: eng publication: Open Mathematics publication_identifier: issn: - 2391-5455 publication_status: published publisher: Walter de Gruyter GmbH status: public title: Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type type: journal_article user_id: '31496' volume: 21 year: '2023' ... --- _id: '53345' abstract: - lang: eng text: 'AbstractA no-flux initial-boundary value problem for

ut=Δ(uϕ(v)),vt=Δv−uv,(⋆)is considered in smoothly bounded subdomains of

with

n⩾1

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

0⩽ξ↦ξα

for some

α⩾1

. Based on the discovery of a gradient structure acting at regularity levels mild enough to be consistent with degeneracy-driven limitations of smoothness information, in this general setting it is shown that with some measurable limit profile

u∞

and some null set

N⋆⊂(0,∞)

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

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

(0,∞)∖N⋆∋t→∞

, where

ρ(ξ):=ξ2(ξ+1)2

ξ⩾0

. In the particular case when either

n⩽2

and

α⩾1

is arbitrary, or

n⩾1

and

α∈[1,2]

, additional quantitative information on the deviation of trajectories from the initial data is derived. This is found to imply a lower estimate for the spatial oscillation of the respective first components throughout evolution, and moreover this is seen to entail that each of the uncountably many steady states

(u⋆,0)

of (

⋆

) is stable with respect to a suitably chosen norm topology.' author: - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Winkler M. Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. Nonlinearity. 2023;36(8):4438-4469. doi:10.1088/1361-6544/ace22e apa: Winkler, M. (2023). Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. Nonlinearity, 36(8), 4438–4469. https://doi.org/10.1088/1361-6544/ace22e bibtex: '@article{Winkler_2023, title={Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction}, volume={36}, DOI={10.1088/1361-6544/ace22e}, number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Winkler, Michael}, year={2023}, pages={4438–4469} }' chicago: 'Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity 36, no. 8 (2023): 4438–69. https://doi.org/10.1088/1361-6544/ace22e.' ieee: 'M. Winkler, “Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction,” Nonlinearity, vol. 36, no. 8, pp. 4438–4469, 2023, doi: 10.1088/1361-6544/ace22e.' mla: Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity, vol. 36, no. 8, IOP Publishing, 2023, pp. 4438–69, doi:10.1088/1361-6544/ace22e. short: M. Winkler, Nonlinearity 36 (2023) 4438–4469. date_created: 2024-04-07T12:56:35Z date_updated: 2024-04-07T12:56:40Z doi: 10.1088/1361-6544/ace22e intvolume: ' 36' issue: '8' keyword: - Applied Mathematics - General Physics and Astronomy - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng page: 4438-4469 publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published publisher: IOP Publishing status: public title: Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction type: journal_article user_id: '31496' volume: 36 year: '2023' ... --- _id: '53341' abstract: - lang: eng text: "AbstractThe Cauchy problem in

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

\r\n \ \r\n \r\n R\r\n \ \r\n n\r\n \ \r\n is considered for the Keller–Segel system

$$\\begin{aligned} \\left\\{ \\begin{array}{l}u_t = \\Delta u - \\nabla \\cdot (u\\nabla v), \\\\ 0 = \\Delta v + u, \\end{array} \\right. \\qquad \\qquad (\\star ) \\end{aligned}$$

\r\n \r\n \ \r\n \r\n \r\n \ \r\n \r\n \ \r\n \r\n \ \r\n \r\n \ \r\n \r\n \ u\r\n t\r\n \ \r\n =\r\n \ Δ\r\n u\r\n \ -\r\n ∇\r\n \ ·\r\n \r\n \ (\r\n u\r\n \ ∇\r\n v\r\n \ )\r\n \r\n \ ,\r\n \r\n \ \r\n \r\n \ \r\n \r\n \ \r\n \r\n 0\r\n =\r\n \ Δ\r\n v\r\n \ +\r\n u\r\n \ ,\r\n \r\n \ \r\n \r\n \ \r\n \r\n \ \r\n \r\n \r\n \r\n \ (\r\n ⋆\r\n \ )\r\n \r\n \ \r\n \r\n \ \r\n \r\n \r\n \ with a focus on a detailed description of behavior in the presence of nonnegative radially symmetric initial data

$$u_0$$

\r\n \r\n \ u\r\n 0\r\n \ \r\n with non-integrable behavior at spatial infinity. It is shown that if

$$u_0$$

\r\n \r\n \ u\r\n 0\r\n \ \r\n is continuous and bounded, then (

$$\\star $$

\r\n \ ⋆\r\n ) admits a local-in-time classical solution, whereas if

$$u_0(x)\\rightarrow +\\infty $$

\r\n \ \r\n \r\n u\r\n \ 0\r\n \r\n \ \r\n (\r\n \ x\r\n )\r\n \ \r\n →\r\n \ +\r\n ∞\r\n \ \r\n as

$$|x|\\rightarrow \\infty $$

\r\n \ \r\n |\r\n x\r\n \ |\r\n →\r\n \ ∞\r\n \r\n , then no such solution can be found. Furthermore, a collection of three sufficient criteria for either global existence or global nonexistence indicates that with respect to the occurrence of finite-time blow-up, spatial decay properties of an explicit singular steady state plays a critical role. In particular, this underlines that explosions in (

$$\\star $$

\r\n \ ⋆\r\n ) need not be enforced by initially high concentrations near finite points, but can be exclusively due to large tails." author: - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Winkler M. Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity. Journal of Elliptic and Parabolic Equations. 2023;9(2):919-959. doi:10.1007/s41808-023-00230-y apa: Winkler, M. (2023). Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity. Journal of Elliptic and Parabolic Equations, 9(2), 919–959. https://doi.org/10.1007/s41808-023-00230-y bibtex: '@article{Winkler_2023, title={Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity}, volume={9}, DOI={10.1007/s41808-023-00230-y}, number={2}, journal={Journal of Elliptic and Parabolic Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2023}, pages={919–959} }' chicago: 'Winkler, Michael. “Solutions to the Keller–Segel System with Non-Integrable Behavior at Spatial Infinity.” Journal of Elliptic and Parabolic Equations 9, no. 2 (2023): 919–59. https://doi.org/10.1007/s41808-023-00230-y.' ieee: 'M. Winkler, “Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity,” Journal of Elliptic and Parabolic Equations, vol. 9, no. 2, pp. 919–959, 2023, doi: 10.1007/s41808-023-00230-y.' mla: Winkler, Michael. “Solutions to the Keller–Segel System with Non-Integrable Behavior at Spatial Infinity.” Journal of Elliptic and Parabolic Equations, vol. 9, no. 2, Springer Science and Business Media LLC, 2023, pp. 919–59, doi:10.1007/s41808-023-00230-y. short: M. Winkler, Journal of Elliptic and Parabolic Equations 9 (2023) 919–959. date_created: 2024-04-07T12:52:52Z date_updated: 2024-04-07T12:52:55Z doi: 10.1007/s41808-023-00230-y intvolume: ' 9' issue: '2' keyword: - Applied Mathematics - Numerical Analysis - Analysis language: - iso: eng page: 919-959 publication: Journal of Elliptic and Parabolic Equations publication_identifier: issn: - 2296-9020 - 2296-9039 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity type: journal_article user_id: '31496' volume: 9 year: '2023' ... --- _id: '53339' abstract: - lang: eng text: "The chemotaxis‐Stokes system \r\n\r\n\r\nis considered along with homogeneous boundary conditions of no‐flux type for \r\n and \r\n, and of Dirichlet type for \r\n, in a smoothly bounded domain \r\n. Under the assumption that \r\n, that \r\n is bounded on each of the intervals \r\n with arbitrary \r\n, and that with some \r\n and \r\n, we have \r\n\r\n\r\nIt is shown that for any suitably regular initial data, an associated initial‐boundary value problem admits a global very weak solution." author: - first_name: Yu full_name: Tian, Yu last_name: Tian - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Tian Y, Winkler M. Keller–Segel–Stokes interaction involving signal‐dependent motilities. Mathematical Methods in the Applied Sciences. 2023;46(14):15667-15683. doi:10.1002/mma.9419 apa: Tian, Y., & Winkler, M. (2023). Keller–Segel–Stokes interaction involving signal‐dependent motilities. Mathematical Methods in the Applied Sciences, 46(14), 15667–15683. https://doi.org/10.1002/mma.9419 bibtex: '@article{Tian_Winkler_2023, title={Keller–Segel–Stokes interaction involving signal‐dependent motilities}, volume={46}, DOI={10.1002/mma.9419}, number={14}, journal={Mathematical Methods in the Applied Sciences}, publisher={Wiley}, author={Tian, Yu and Winkler, Michael}, year={2023}, pages={15667–15683} }' chicago: 'Tian, Yu, and Michael Winkler. “Keller–Segel–Stokes Interaction Involving Signal‐dependent Motilities.” Mathematical Methods in the Applied Sciences 46, no. 14 (2023): 15667–83. https://doi.org/10.1002/mma.9419.' ieee: 'Y. Tian and M. Winkler, “Keller–Segel–Stokes interaction involving signal‐dependent motilities,” Mathematical Methods in the Applied Sciences, vol. 46, no. 14, pp. 15667–15683, 2023, doi: 10.1002/mma.9419.' mla: Tian, Yu, and Michael Winkler. “Keller–Segel–Stokes Interaction Involving Signal‐dependent Motilities.” Mathematical Methods in the Applied Sciences, vol. 46, no. 14, Wiley, 2023, pp. 15667–83, doi:10.1002/mma.9419. short: Y. Tian, M. Winkler, Mathematical Methods in the Applied Sciences 46 (2023) 15667–15683. date_created: 2024-04-07T12:51:27Z date_updated: 2024-04-07T12:51:31Z doi: 10.1002/mma.9419 intvolume: ' 46' issue: '14' keyword: - General Engineering - General Mathematics language: - iso: eng page: 15667-15683 publication: Mathematical Methods in the Applied Sciences publication_identifier: issn: - 0170-4214 - 1099-1476 publication_status: published publisher: Wiley status: public title: Keller–Segel–Stokes interaction involving signal‐dependent motilities type: journal_article user_id: '31496' volume: 46 year: '2023' ... --- _id: '53340' author: - first_name: Kevin J. full_name: Painter, Kevin J. last_name: Painter - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Painter KJ, Winkler M. Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. SIAM Journal on Applied Mathematics. 2023;83(5):2096-2117. doi:10.1137/22m1539393 apa: Painter, K. J., & Winkler, M. (2023). Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. SIAM Journal on Applied Mathematics, 83(5), 2096–2117. https://doi.org/10.1137/22m1539393 bibtex: '@article{Painter_Winkler_2023, title={Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}, volume={83}, DOI={10.1137/22m1539393}, number={5}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Painter, Kevin J. and Winkler, Michael}, year={2023}, pages={2096–2117} }' chicago: 'Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” SIAM Journal on Applied Mathematics 83, no. 5 (2023): 2096–2117. https://doi.org/10.1137/22m1539393.' ieee: 'K. J. Painter and M. Winkler, “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities,” SIAM Journal on Applied Mathematics, vol. 83, no. 5, pp. 2096–2117, 2023, doi: 10.1137/22m1539393.' mla: Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” SIAM Journal on Applied Mathematics, vol. 83, no. 5, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 2096–117, doi:10.1137/22m1539393. short: K.J. Painter, M. Winkler, SIAM Journal on Applied Mathematics 83 (2023) 2096–2117. date_created: 2024-04-07T12:52:03Z date_updated: 2024-04-07T12:52:06Z doi: 10.1137/22m1539393 intvolume: ' 83' issue: '5' keyword: - Applied Mathematics language: - iso: eng page: 2096-2117 publication: SIAM Journal on Applied Mathematics publication_identifier: issn: - 0036-1399 - 1095-712X publication_status: published publisher: Society for Industrial & Applied Mathematics (SIAM) status: public title: Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities type: journal_article user_id: '31496' volume: 83 year: '2023' ... --- _id: '53342' author: - first_name: Michael full_name: Winkler, Michael last_name: Winkler - first_name: Tomomi full_name: Yokota, Tomomi last_name: Yokota citation: ama: Winkler M, Yokota T. Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems. Journal of Differential Equations. 2023;374:1-28. doi:10.1016/j.jde.2023.07.029 apa: Winkler, M., & Yokota, T. (2023). Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems. Journal of Differential Equations, 374, 1–28. https://doi.org/10.1016/j.jde.2023.07.029 bibtex: '@article{Winkler_Yokota_2023, title={Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems}, volume={374}, DOI={10.1016/j.jde.2023.07.029}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler, Michael and Yokota, Tomomi}, year={2023}, pages={1–28} }' chicago: 'Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena by Arbitrarily Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes Systems.” Journal of Differential Equations 374 (2023): 1–28. https://doi.org/10.1016/j.jde.2023.07.029.' ieee: 'M. Winkler and T. Yokota, “Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems,” Journal of Differential Equations, vol. 374, pp. 1–28, 2023, doi: 10.1016/j.jde.2023.07.029.' mla: Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena by Arbitrarily Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes Systems.” Journal of Differential Equations, vol. 374, Elsevier BV, 2023, pp. 1–28, doi:10.1016/j.jde.2023.07.029. short: M. Winkler, T. Yokota, Journal of Differential Equations 374 (2023) 1–28. date_created: 2024-04-07T12:53:32Z date_updated: 2024-04-07T12:53:38Z doi: 10.1016/j.jde.2023.07.029 intvolume: ' 374' keyword: - Analysis - Applied Mathematics language: - iso: eng page: 1-28 publication: Journal of Differential Equations publication_identifier: issn: - 0022-0396 publication_status: published publisher: Elsevier BV status: public title: Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems type: journal_article user_id: '31496' volume: 374 year: '2023' ... --- _id: '53346' author: - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Winkler M. Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing. Advances in Differential Equations. 2023;28(11/12). doi:10.57262/ade028-1112-921 apa: Winkler, M. (2023). Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing. Advances in Differential Equations, 28(11/12). https://doi.org/10.57262/ade028-1112-921 bibtex: '@article{Winkler_2023, title={Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing}, volume={28}, DOI={10.57262/ade028-1112-921}, number={11/12}, journal={Advances in Differential Equations}, publisher={Khayyam Publishing, Inc}, author={Winkler, Michael}, year={2023} }' chicago: Winkler, Michael. “Absence of Collapse into Persistent Dirac-Type Singularities in a Keller-Segel-Navier-Stokes System Involving Local Sensing.” Advances in Differential Equations 28, no. 11/12 (2023). https://doi.org/10.57262/ade028-1112-921. ieee: 'M. Winkler, “Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing,” Advances in Differential Equations, vol. 28, no. 11/12, 2023, doi: 10.57262/ade028-1112-921.' mla: Winkler, Michael. “Absence of Collapse into Persistent Dirac-Type Singularities in a Keller-Segel-Navier-Stokes System Involving Local Sensing.” Advances in Differential Equations, vol. 28, no. 11/12, Khayyam Publishing, Inc, 2023, doi:10.57262/ade028-1112-921. short: M. Winkler, Advances in Differential Equations 28 (2023). date_created: 2024-04-07T12:57:19Z date_updated: 2024-04-07T12:57:23Z doi: 10.57262/ade028-1112-921 intvolume: ' 28' issue: 11/12 keyword: - Applied Mathematics - Analysis language: - iso: eng publication: Advances in Differential Equations publication_identifier: issn: - 1079-9389 publication_status: published publisher: Khayyam Publishing, Inc status: public title: Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing type: journal_article user_id: '31496' volume: 28 year: '2023' ... --- _id: '45984' author: - first_name: Mannat full_name: Kaur, Mannat last_name: Kaur - first_name: Harshini full_name: Sri Ramulu, Harshini id: '99000' last_name: Sri Ramulu orcid: 0000-0002-0000-5843 - first_name: Yasemin full_name: Acar, Yasemin last_name: Acar - first_name: Tobias full_name: Fiebig, Tobias last_name: Fiebig citation: ama: 'Kaur M, Sri Ramulu H, Acar Y, Fiebig T. “Oh yes! over-preparing for meetings is my jam :)”: The Gendered Experiences of System Administrators. Proc ACM Hum Comput Interact. 2023;7(CSCW1):1–38. doi:10.1145/3579617' apa: 'Kaur, M., Sri Ramulu, H., Acar, Y., & Fiebig, T. (2023). “Oh yes! over-preparing for meetings is my jam :)”: The Gendered Experiences of System Administrators. Proc. ACM Hum. Comput. Interact., 7(CSCW1), 1–38. https://doi.org/10.1145/3579617' bibtex: '@article{Kaur_Sri Ramulu_Acar_Fiebig_2023, title={“Oh yes! over-preparing for meetings is my jam :)”: The Gendered Experiences of System Administrators}, volume={7}, DOI={10.1145/3579617}, number={CSCW1}, journal={Proc. ACM Hum. Comput. Interact.}, author={Kaur, Mannat and Sri Ramulu, Harshini and Acar, Yasemin and Fiebig, Tobias}, year={2023}, pages={1–38} }' chicago: 'Kaur, Mannat, Harshini Sri Ramulu, Yasemin Acar, and Tobias Fiebig. “‘Oh Yes! Over-Preparing for Meetings Is My Jam :)’: The Gendered Experiences of System Administrators.” Proc. ACM Hum. Comput. Interact. 7, no. CSCW1 (2023): 1–38. https://doi.org/10.1145/3579617.' ieee: 'M. Kaur, H. Sri Ramulu, Y. Acar, and T. Fiebig, “‘Oh yes! over-preparing for meetings is my jam :)’: The Gendered Experiences of System Administrators,” Proc. ACM Hum. Comput. Interact., vol. 7, no. CSCW1, pp. 1–38, 2023, doi: 10.1145/3579617.' mla: 'Kaur, Mannat, et al. “‘Oh Yes! Over-Preparing for Meetings Is My Jam :)’: The Gendered Experiences of System Administrators.” Proc. ACM Hum. Comput. Interact., vol. 7, no. CSCW1, 2023, pp. 1–38, doi:10.1145/3579617.' short: M. Kaur, H. Sri Ramulu, Y. Acar, T. Fiebig, Proc. ACM Hum. Comput. Interact. 7 (2023) 1–38. date_created: 2023-07-11T06:23:54Z date_updated: 2024-04-09T07:19:23Z doi: 10.1145/3579617 intvolume: ' 7' issue: CSCW1 language: - iso: eng page: 1–38 publication: Proc. ACM Hum. Comput. Interact. status: public title: '"Oh yes! over-preparing for meetings is my jam :)": The Gendered Experiences of System Administrators' type: journal_article user_id: '15458' volume: 7 year: '2023' ... --- _id: '51101' author: - first_name: Gerda full_name: Werth, Gerda id: '578' last_name: Werth citation: ama: 'Werth G. Neue Wege Im Mathematischen Unterricht: Auf Den Spuren Mathilde Vaertings. Springer Fachmedien Wiesbaden; 2023. doi:10.1007/978-3-658-42445-9' apa: 'Werth, G. (2023). Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings. Springer Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-42445-9' bibtex: '@book{Werth_2023, place={Wiesbaden}, title={Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings}, DOI={10.1007/978-3-658-42445-9}, publisher={Springer Fachmedien Wiesbaden}, author={Werth, Gerda}, year={2023} }' chicago: 'Werth, Gerda. Neue Wege Im Mathematischen Unterricht: Auf Den Spuren Mathilde Vaertings. Wiesbaden: Springer Fachmedien Wiesbaden, 2023. https://doi.org/10.1007/978-3-658-42445-9.' ieee: 'G. Werth, Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings. Wiesbaden: Springer Fachmedien Wiesbaden, 2023.' mla: 'Werth, Gerda. Neue Wege Im Mathematischen Unterricht: Auf Den Spuren Mathilde Vaertings. Springer Fachmedien Wiesbaden, 2023, doi:10.1007/978-3-658-42445-9.' short: 'G. Werth, Neue Wege Im Mathematischen Unterricht: Auf Den Spuren Mathilde Vaertings, Springer Fachmedien Wiesbaden, Wiesbaden, 2023.' date_created: 2024-01-31T13:08:37Z date_updated: 2024-04-09T11:07:16Z department: - _id: '34' - _id: '10' - _id: '98' - _id: '360' doi: 10.1007/978-3-658-42445-9 language: - iso: eng place: Wiesbaden publication_identifier: isbn: - '9783658424442' - '9783658424459' issn: - 2661-8591 - 2661-8605 publication_status: published publisher: Springer Fachmedien Wiesbaden status: public title: 'Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings' type: book user_id: '578' year: '2023' ... --- _id: '51103' author: - first_name: Gerda full_name: Werth, Gerda id: '578' last_name: Werth citation: ama: Werth G. Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe. mathematik lehren. 2023;241:15-19. apa: Werth, G. (2023). Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe. mathematik lehren, 241, 15–19. bibtex: '@article{Werth_2023, title={Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe}, volume={241}, journal={mathematik lehren}, publisher={Friedrich}, author={Werth, Gerda}, year={2023}, pages={15–19} }' chicago: 'Werth, Gerda. “Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe.” mathematik lehren 241 (2023): 15–19.' ieee: G. Werth, “Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe,” mathematik lehren, vol. 241, pp. 15–19, 2023. mla: Werth, Gerda. “Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe.” mathematik lehren, vol. 241, Friedrich, 2023, pp. 15–19. short: G. Werth, mathematik lehren 241 (2023) 15–19. date_created: 2024-01-31T13:15:50Z date_updated: 2024-04-09T09:19:05Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '360' intvolume: ' 241' language: - iso: ger page: 15-19 publication: mathematik lehren publication_status: published publisher: Friedrich status: public title: Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe type: journal_article user_id: '578' volume: 241 year: '2023' ... --- _id: '51739' author: - first_name: Deborah full_name: Weiß, Deborah id: '45673' last_name: Weiß - first_name: Tobias full_name: Duffe, Tobias id: '41322' last_name: Duffe - first_name: Moritz full_name: Buczek, Moritz id: '83727' last_name: Buczek - first_name: Gunter full_name: Kullmer, Gunter id: '291' last_name: Kullmer - first_name: Britta full_name: Schramm, Britta id: '4668' last_name: Schramm citation: ama: 'Weiß D, Duffe T, Buczek M, Kullmer G, Schramm B. Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss. In: Deutscher Verband für Materialforschung und -prüfung e.V.; 2023. doi:10.48447/WP-2023-244' apa: 'Weiß, D., Duffe, T., Buczek, M., Kullmer, G., & Schramm, B. (2023). Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss. Werkstoffprüfung 2023: Werkstoffe und Bauteile auf dem Prüfstand - Tagung, Berlin. https://doi.org/10.48447/WP-2023-244' bibtex: '@inproceedings{Weiß_Duffe_Buczek_Kullmer_Schramm_2023, title={Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss}, DOI={10.48447/WP-2023-244}, publisher={Deutscher Verband für Materialforschung und -prüfung e.V.}, author={Weiß, Deborah and Duffe, Tobias and Buczek, Moritz and Kullmer, Gunter and Schramm, Britta}, year={2023} }' chicago: Weiß, Deborah, Tobias Duffe, Moritz Buczek, Gunter Kullmer, and Britta Schramm. “Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss.” Deutscher Verband für Materialforschung und -prüfung e.V., 2023. https://doi.org/10.48447/WP-2023-244. ieee: 'D. Weiß, T. Duffe, M. Buczek, G. Kullmer, and B. Schramm, “Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss,” presented at the Werkstoffprüfung 2023: Werkstoffe und Bauteile auf dem Prüfstand - Tagung, Berlin, 2023, doi: 10.48447/WP-2023-244.' mla: Weiß, Deborah, et al. Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss. Deutscher Verband für Materialforschung und -prüfung e.V., 2023, doi:10.48447/WP-2023-244. short: 'D. Weiß, T. Duffe, M. Buczek, G. Kullmer, B. Schramm, in: Deutscher Verband für Materialforschung und -prüfung e.V., 2023.' conference: end_date: 2023-11-24 location: Berlin name: 'Werkstoffprüfung 2023: Werkstoffe und Bauteile auf dem Prüfstand - Tagung' start_date: 2023-11-23 date_created: 2024-02-22T09:54:40Z date_updated: 2024-04-10T07:08:49Z department: - _id: '143' - _id: '630' doi: 10.48447/WP-2023-244 language: - iso: ger project: - _id: '130' grant_number: '418701707' name: 'TRR 285: TRR 285' - _id: '132' name: 'TRR 285 - B: TRR 285 - Project Area B' - _id: '143' name: 'TRR 285 – B04: TRR 285 - Subproject B04' publication_status: published publisher: Deutscher Verband für Materialforschung und -prüfung e.V. status: public title: Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss type: conference user_id: '45673' year: '2023' ... --- _id: '35904' author: - first_name: Lydia full_name: Böttger, Lydia id: '65153' last_name: Böttger - first_name: Constanze full_name: Niederhaus, Constanze id: '54999' last_name: Niederhaus citation: ama: 'Böttger L, Niederhaus C. CLIL - Content and Language Integrated Learning. In: Efing C, Kalkavan-Aydin Z, eds. Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive. De Gruyter; 2023. doi:https://doi.org/10.1515/9783110745504' apa: Böttger, L., & Niederhaus, C. (2023). CLIL - Content and Language Integrated Learning. In C. Efing & Z. Kalkavan-Aydin (Eds.), Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive. De Gruyter. https://doi.org/10.1515/9783110745504 bibtex: '@inbook{Böttger_Niederhaus_2023, place={Berlin/Boston}, title={CLIL - Content and Language Integrated Learning}, DOI={https://doi.org/10.1515/9783110745504}, booktitle={Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive}, publisher={De Gruyter}, author={Böttger, Lydia and Niederhaus, Constanze}, editor={Efing, Christian and Kalkavan-Aydin, Zeynep}, year={2023} }' chicago: 'Böttger, Lydia, and Constanze Niederhaus. “CLIL - Content and Language Integrated Learning.” In Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive, edited by Christian Efing and Zeynep Kalkavan-Aydin. Berlin/Boston: De Gruyter, 2023. https://doi.org/10.1515/9783110745504.' ieee: 'L. Böttger and C. Niederhaus, “CLIL - Content and Language Integrated Learning,” in Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive, C. Efing and Z. Kalkavan-Aydin, Eds. Berlin/Boston: De Gruyter, 2023.' mla: Böttger, Lydia, and Constanze Niederhaus. “CLIL - Content and Language Integrated Learning.” Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive, edited by Christian Efing and Zeynep Kalkavan-Aydin, De Gruyter, 2023, doi:https://doi.org/10.1515/9783110745504. short: 'L. Böttger, C. Niederhaus, in: C. Efing, Z. Kalkavan-Aydin (Eds.), Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive, De Gruyter, Berlin/Boston, 2023.' date_created: 2023-01-10T23:28:10Z date_updated: 2024-04-10T14:59:38Z department: - _id: '5' doi: https://doi.org/10.1515/9783110745504 editor: - first_name: Christian full_name: Efing, Christian last_name: Efing - first_name: Zeynep full_name: Kalkavan-Aydin, Zeynep last_name: Kalkavan-Aydin language: - iso: ger place: Berlin/Boston publication: Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive publication_status: published publisher: De Gruyter status: public title: CLIL - Content and Language Integrated Learning type: book_chapter user_id: '65153' year: '2023' ... --- _id: '53404' 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." author: - first_name: Lasse L. full_name: Wolf, Lasse L. last_name: Wolf - first_name: Hong-Wei full_name: Zhang, Hong-Wei last_name: Zhang 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. 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} }' 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. 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. 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). date_created: 2024-04-10T13:45:59Z date_updated: 2024-04-10T13:48:17Z department: - _id: '10' - _id: '548' external_id: arxiv: - '2311.11770' language: - iso: eng publication: arXiv:2311.11770 status: public title: $L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces type: preprint user_id: '45027' year: '2023' ... --- _id: '53405' abstract: - lang: eng 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." author: - first_name: Tobias full_name: Jenert, Tobias id: '71994' last_name: Jenert orcid: ' https://orcid.org/0000-0001-9262-5646' 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.' 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. 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} }' 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.' date_created: 2024-04-11T06:29:37Z date_updated: 2024-04-11T06:30:05Z department: - _id: '208' editor: - first_name: H.-Hugo full_name: Kremer, H.-Hugo last_name: Kremer - first_name: Hubert full_name: Ertl, Hubert last_name: Ertl - first_name: Peter F. E. full_name: Sloane, Peter F. E. last_name: Sloane language: - iso: eng main_file_link: - url: https://www.bibb.de/dienst/publikationen/de/download/18616 page: 11-24 place: Bonn publication: Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung publisher: Bundesinstitut für Berufsbildung. quality_controlled: '1' status: public title: Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis type: book_chapter user_id: '71994' year: '2023' ... --- _id: '52380' author: - first_name: Sören full_name: Sparmann, Sören id: '63216' last_name: Sparmann - first_name: Sven full_name: Hüsing, Sven id: '58465' last_name: Hüsing - first_name: Carsten full_name: Schulte, Carsten id: '60311' last_name: Schulte citation: 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' 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} }' 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.' 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.' 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.' short: 'S. Sparmann, S. Hüsing, C. Schulte, in: Proceedings of the 23rd Koli Calling International Conference on Computing Education Research, ACM, 2023.' date_created: 2024-03-08T08:02:10Z date_updated: 2024-04-11T12:30:59Z department: - _id: '67' doi: 10.1145/3631802.3631824 language: - iso: eng publication: Proceedings of the 23rd Koli Calling International Conference on Computing Education Research publication_status: published publisher: ACM status: public title: 'JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks' type: conference user_id: '58465' year: '2023' ... --- _id: '53410' abstract: - lang: eng text: AbstractWe consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing, the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016) can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane. author: - first_name: Benjamin full_name: Delarue, Benjamin id: '70575' last_name: Delarue - first_name: Philipp full_name: Schütte, Philipp id: '50168' last_name: Schütte - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Delarue B, Schütte P, Weich T. Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. Annales Henri Poincaré. 2023;25(2):1607-1656. doi:10.1007/s00023-023-01379-x apa: Delarue, B., Schütte, P., & Weich, T. (2023). Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. Annales Henri Poincaré, 25(2), 1607–1656. https://doi.org/10.1007/s00023-023-01379-x bibtex: '@article{Delarue_Schütte_Weich_2023, title={Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}, volume={25}, DOI={10.1007/s00023-023-01379-x}, number={2}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}, year={2023}, pages={1607–1656} }' chicago: 'Delarue, Benjamin, Philipp Schütte, and Tobias Weich. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” Annales Henri Poincaré 25, no. 2 (2023): 1607–56. https://doi.org/10.1007/s00023-023-01379-x.' ieee: 'B. Delarue, P. Schütte, and T. Weich, “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” Annales Henri Poincaré, vol. 25, no. 2, pp. 1607–1656, 2023, doi: 10.1007/s00023-023-01379-x.' mla: Delarue, Benjamin, et al. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” Annales Henri Poincaré, vol. 25, no. 2, Springer Science and Business Media LLC, 2023, pp. 1607–56, doi:10.1007/s00023-023-01379-x. short: B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656. date_created: 2024-04-11T12:30:14Z date_updated: 2024-04-11T12:37:34Z department: - _id: '548' doi: 10.1007/s00023-023-01379-x intvolume: ' 25' issue: '2' keyword: - Mathematical Physics - Nuclear and High Energy Physics - Statistical and Nonlinear Physics language: - iso: eng page: 1607-1656 publication: Annales Henri Poincaré publication_identifier: issn: - 1424-0637 - 1424-0661 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models type: journal_article user_id: '70575' volume: 25 year: '2023' ...