--- _id: '53315' abstract: - lang: eng text: "AbstractIn a smoothly bounded two‐dimensional domain and for a given nondecreasing positive unbounded , for each and the inequality\r\nis shown to hold for any positive fulfilling\r\nThis is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over near its explosion time." author: - first_name: Yulan full_name: Wang, Yulan last_name: Wang - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Wang Y, Winkler M. An interpolation inequality involving $L\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. Journal of the London Mathematical Society. 2024;109(3). doi:10.1112/jlms.12885 apa: Wang, Y., & Winkler, M. (2024). An interpolation inequality involving $L\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. Journal of the London Mathematical Society, 109(3). https://doi.org/10.1112/jlms.12885 bibtex: '@article{Wang_Winkler_2024, title={An interpolation inequality involving $L\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={10.1112/jlms.12885}, number={3}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024} }' chicago: Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” Journal of the London Mathematical Society 109, no. 3 (2024). https://doi.org/10.1112/jlms.12885. ieee: 'Y. Wang and M. Winkler, “An interpolation inequality involving $L\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system,” Journal of the London Mathematical Society, vol. 109, no. 3, 2024, doi: 10.1112/jlms.12885.' mla: Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” Journal of the London Mathematical Society, vol. 109, no. 3, Wiley, 2024, doi:10.1112/jlms.12885. short: Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024). date_created: 2024-04-07T12:27:28Z date_updated: 2024-04-07T12:36:25Z doi: 10.1112/jlms.12885 intvolume: ' 109' issue: '3' keyword: - General Mathematics language: - iso: eng publication: Journal of the London Mathematical Society publication_identifier: issn: - 0024-6107 - 1469-7750 publication_status: published publisher: Wiley status: public title: An interpolation inequality involving $L\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system type: journal_article user_id: '31496' volume: 109 year: '2024' ... --- _id: '45971' abstract: - lang: eng text: "Abstract\r\n An error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unit-length constraints. The analysis is based on elementary approximation results and only uses the discrete weak formulation." author: - first_name: Sören full_name: Bartels, Sören last_name: Bartels - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 - first_name: Zhangxian full_name: Wang, Zhangxian last_name: Wang citation: ama: Bartels S, Kovács B, Wang Z. Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints. IMA Journal of Numerical Analysis. Published online 2023. doi:10.1093/imanum/drad037 apa: Bartels, S., Kovács, B., & Wang, Z. (2023). Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drad037 bibtex: '@article{Bartels_Kovács_Wang_2023, title={Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints}, DOI={10.1093/imanum/drad037}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Bartels, Sören and Kovács, Balázs and Wang, Zhangxian}, year={2023} }' chicago: Bartels, Sören, Balázs Kovács, and Zhangxian Wang. “Error Analysis for the Numerical Approximation of the Harmonic Map Heat Flow with Nodal Constraints.” IMA Journal of Numerical Analysis, 2023. https://doi.org/10.1093/imanum/drad037. ieee: 'S. Bartels, B. Kovács, and Z. Wang, “Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints,” IMA Journal of Numerical Analysis, 2023, doi: 10.1093/imanum/drad037.' mla: Bartels, Sören, et al. “Error Analysis for the Numerical Approximation of the Harmonic Map Heat Flow with Nodal Constraints.” IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2023, doi:10.1093/imanum/drad037. short: S. Bartels, B. Kovács, Z. Wang, IMA Journal of Numerical Analysis (2023). date_created: 2023-07-10T12:32:10Z date_updated: 2024-04-03T09:15:27Z department: - _id: '841' doi: 10.1093/imanum/drad037 keyword: - Applied Mathematics - Computational Mathematics - General Mathematics language: - iso: eng publication: IMA Journal of Numerical Analysis publication_identifier: issn: - 0272-4979 - 1464-3642 publication_status: published publisher: Oxford University Press (OUP) status: public title: Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints type: journal_article user_id: '100441' 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: '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: '53538' abstract: - lang: eng text: AbstractWe study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the hyperbolic plane. author: - first_name: G. full_name: Polychrou, G. last_name: Polychrou - first_name: Efthymia full_name: Papageorgiou, Efthymia id: '100325' last_name: Papageorgiou - first_name: A. full_name: Fotiadis, A. last_name: Fotiadis - first_name: C. full_name: Daskaloyannis, C. last_name: Daskaloyannis citation: ama: Polychrou G, Papageorgiou E, Fotiadis A, Daskaloyannis C. New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation. Revista Matemática Complutense. Published online 2023. doi:10.1007/s13163-023-00476-z apa: Polychrou, G., Papageorgiou, E., Fotiadis, A., & Daskaloyannis, C. (2023). New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation. Revista Matemática Complutense. https://doi.org/10.1007/s13163-023-00476-z bibtex: '@article{Polychrou_Papageorgiou_Fotiadis_Daskaloyannis_2023, title={New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation}, DOI={10.1007/s13163-023-00476-z}, journal={Revista Matemática Complutense}, publisher={Springer Science and Business Media LLC}, author={Polychrou, G. and Papageorgiou, Efthymia and Fotiadis, A. and Daskaloyannis, C.}, year={2023} }' chicago: Polychrou, G., Efthymia Papageorgiou, A. Fotiadis, and C. Daskaloyannis. “New Examples of Harmonic Maps to the Hyperbolic Plane via Bäcklund Transformation.” Revista Matemática Complutense, 2023. https://doi.org/10.1007/s13163-023-00476-z. ieee: 'G. Polychrou, E. Papageorgiou, A. Fotiadis, and C. Daskaloyannis, “New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation,” Revista Matemática Complutense, 2023, doi: 10.1007/s13163-023-00476-z.' mla: Polychrou, G., et al. “New Examples of Harmonic Maps to the Hyperbolic Plane via Bäcklund Transformation.” Revista Matemática Complutense, Springer Science and Business Media LLC, 2023, doi:10.1007/s13163-023-00476-z. short: G. Polychrou, E. Papageorgiou, A. Fotiadis, C. Daskaloyannis, Revista Matemática Complutense (2023). date_created: 2024-04-17T13:15:07Z date_updated: 2024-04-17T13:15:51Z department: - _id: '555' doi: 10.1007/s13163-023-00476-z keyword: - General Mathematics language: - iso: eng publication: Revista Matemática Complutense publication_identifier: issn: - 1139-1138 - 1988-2807 publication_status: published publisher: Springer Science and Business Media LLC status: public title: New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation type: journal_article user_id: '100325' year: '2023' ... --- _id: '45786' abstract: - lang: eng text: Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “interface ePortfolio” in the context of a geometry course for preservice teachers (PSTs). The tool offers the possibility of implementing the design principle of profession orientation. In the article, we theoretically clarify what we understand by this principle and locate our innovative concept against this theoretical background. We empirically investigate the extent to which counteraction against the second discontinuity is successful by analyzing reflection texts created in the interface ePortfolio, focusing on PSTs’ perspectives. Our qualitative content analysis shows that most of them perceive the innovation as helpful in the intended sense and indicates that the course concept, in general, and the interface ePortfolio, in particular, have helped establish relevant links between the course content and their later work as teachers. article_type: original author: - first_name: Max full_name: Hoffmann, Max id: '32202' last_name: Hoffmann orcid: 0000-0002-6964-7123 - first_name: Rolf full_name: Biehler, Rolf id: '16274' last_name: Biehler citation: ama: Hoffmann M, Biehler R. Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course. ZDM – Mathematics Education. Published online 2023. doi:10.1007/s11858-023-01505-3 apa: Hoffmann, M., & Biehler, R. (2023). Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-023-01505-3 bibtex: '@article{Hoffmann_Biehler_2023, title={Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course}, DOI={10.1007/s11858-023-01505-3}, journal={ZDM – Mathematics Education}, publisher={Springer}, author={Hoffmann, Max and Biehler, Rolf}, year={2023} }' chicago: Hoffmann, Max, and Rolf Biehler. “Implementing Profession Orientation as a Design Principle for Overcoming Klein’s Second Discontinuity – Preservice Teacher’s Perspectives on Interface Activities in the Context of a Geometry Course.” ZDM – Mathematics Education, 2023. https://doi.org/10.1007/s11858-023-01505-3. ieee: 'M. Hoffmann and R. Biehler, “Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course,” ZDM – Mathematics Education, 2023, doi: 10.1007/s11858-023-01505-3.' mla: Hoffmann, Max, and Rolf Biehler. “Implementing Profession Orientation as a Design Principle for Overcoming Klein’s Second Discontinuity – Preservice Teacher’s Perspectives on Interface Activities in the Context of a Geometry Course.” ZDM – Mathematics Education, Springer, 2023, doi:10.1007/s11858-023-01505-3. short: M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2023). date_created: 2023-06-27T11:45:25Z date_updated: 2024-04-18T09:01:29Z ddc: - '510' - '370' department: - _id: '643' doi: 10.1007/s11858-023-01505-3 file: - access_level: closed content_type: application/pdf creator: maxh date_created: 2023-07-13T09:40:02Z date_updated: 2023-07-13T09:40:02Z file_id: '46041' file_name: s11858-023-01505-3.pdf file_size: 1460246 relation: main_file success: 1 file_date_updated: 2023-07-13T09:40:02Z has_accepted_license: '1' keyword: - General Mathematics - Education language: - iso: eng main_file_link: - open_access: '1' url: https://link.springer.com/article/10.1007/s11858-023-01505-3 oa: '1' publication: ZDM – Mathematics Education publication_identifier: issn: - 1863-9690 - 1863-9704 publication_status: published publisher: Springer quality_controlled: '1' status: public title: Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course type: journal_article user_id: '37888' year: '2023' ... --- _id: '46569' abstract: - lang: eng text: 'AbstractExternal visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to characterize external visualizations in recent mathematics education research in order to develop a common ground and guide future research. A qualitative content analysis of the full texts of 130 studies published between 2018 and 2022 applied a deductive-inductive coding procedure to assess four dimensions: visualization product or process, type of visualization, media, and purpose. The analysis revealed different types of external visualizations including visualizations with physical resemblance ranging from pictorial to abstract visualizations as well as three types of visualizations with structural resemblance: length, area, and relational visualizations. Future research should include measures of visualization products or processes to help explain the demands and affordances that different types of visualizations present to learners and teachers.' author: - first_name: Johanna full_name: Schoenherr, Johanna last_name: Schoenherr - first_name: Stanislaw full_name: Schukajlow, Stanislaw last_name: Schukajlow citation: ama: 'Schoenherr J, Schukajlow S. Characterizing external visualization in mathematics education research: a scoping review. ZDM – Mathematics Education. Published online 2023. doi:10.1007/s11858-023-01494-3' apa: 'Schoenherr, J., & Schukajlow, S. (2023). Characterizing external visualization in mathematics education research: a scoping review. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-023-01494-3' bibtex: '@article{Schoenherr_Schukajlow_2023, title={Characterizing external visualization in mathematics education research: a scoping review}, DOI={10.1007/s11858-023-01494-3}, journal={ZDM – Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Schoenherr, Johanna and Schukajlow, Stanislaw}, year={2023} }' chicago: 'Schoenherr, Johanna, and Stanislaw Schukajlow. “Characterizing External Visualization in Mathematics Education Research: A Scoping Review.” ZDM – Mathematics Education, 2023. https://doi.org/10.1007/s11858-023-01494-3.' ieee: 'J. Schoenherr and S. Schukajlow, “Characterizing external visualization in mathematics education research: a scoping review,” ZDM – Mathematics Education, 2023, doi: 10.1007/s11858-023-01494-3.' mla: 'Schoenherr, Johanna, and Stanislaw Schukajlow. “Characterizing External Visualization in Mathematics Education Research: A Scoping Review.” ZDM – Mathematics Education, Springer Science and Business Media LLC, 2023, doi:10.1007/s11858-023-01494-3.' short: J. Schoenherr, S. Schukajlow, ZDM – Mathematics Education (2023). date_created: 2023-08-17T10:11:45Z date_updated: 2024-04-30T13:43:22Z department: - _id: '913' doi: 10.1007/s11858-023-01494-3 keyword: - General Mathematics - Education language: - iso: eng publication: ZDM – Mathematics Education publication_identifier: issn: - 1863-9690 - 1863-9704 publication_status: published publisher: Springer Science and Business Media LLC status: public title: 'Characterizing external visualization in mathematics education research: a scoping review' type: journal_article user_id: '99409' year: '2023' ... --- _id: '53533' author: - first_name: Alena full_name: Ernst, Alena id: '46953' last_name: Ernst - first_name: Kai-Uwe full_name: Schmidt, Kai-Uwe last_name: Schmidt citation: ama: Ernst A, Schmidt K-U. Intersection theorems for finite general linear groups. Mathematical Proceedings of the Cambridge Philosophical Society. 2023;175(1):129-160. doi:10.1017/s0305004123000075 apa: Ernst, A., & Schmidt, K.-U. (2023). Intersection theorems for finite general linear groups. Mathematical Proceedings of the Cambridge Philosophical Society, 175(1), 129–160. https://doi.org/10.1017/s0305004123000075 bibtex: '@article{Ernst_Schmidt_2023, title={Intersection theorems for finite general linear groups}, volume={175}, DOI={10.1017/s0305004123000075}, number={1}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Ernst, Alena and Schmidt, Kai-Uwe}, year={2023}, pages={129–160} }' chicago: 'Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” Mathematical Proceedings of the Cambridge Philosophical Society 175, no. 1 (2023): 129–60. https://doi.org/10.1017/s0305004123000075.' ieee: 'A. Ernst and K.-U. Schmidt, “Intersection theorems for finite general linear groups,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 175, no. 1, pp. 129–160, 2023, doi: 10.1017/s0305004123000075.' mla: Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 175, no. 1, Cambridge University Press (CUP), 2023, pp. 129–60, doi:10.1017/s0305004123000075. short: A. Ernst, K.-U. Schmidt, Mathematical Proceedings of the Cambridge Philosophical Society 175 (2023) 129–160. date_created: 2024-04-17T12:23:18Z date_updated: 2024-05-07T08:29:59Z department: - _id: '100' doi: 10.1017/s0305004123000075 intvolume: ' 175' issue: '1' keyword: - General Mathematics language: - iso: eng page: 129-160 publication: Mathematical Proceedings of the Cambridge Philosophical Society publication_identifier: issn: - 0305-0041 - 1469-8064 publication_status: published publisher: Cambridge University Press (CUP) status: public title: Intersection theorems for finite general linear groups type: journal_article user_id: '46953' volume: 175 year: '2023' ... --- _id: '46256' author: - first_name: Yulai full_name: Ma, Yulai id: '92748' last_name: Ma - first_name: Davide full_name: Mattiolo, Davide last_name: Mattiolo - first_name: Eckhard full_name: Steffen, Eckhard id: '15548' last_name: Steffen orcid: 0000-0002-9808-7401 - first_name: Isaak Hieronymus full_name: Wolf, Isaak Hieronymus id: '88145' last_name: Wolf citation: ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics. 2023;37(3):1548-1565. doi:10.1137/22m1500654 apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics, 37(3), 1548–1565. https://doi.org/10.1137/22m1500654 bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={10.1137/22m1500654}, number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565} }' chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics 37, no. 3 (2023): 1548–65. https://doi.org/10.1137/22m1500654.' ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs,” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, pp. 1548–1565, 2023, doi: 10.1137/22m1500654.' mla: Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:10.1137/22m1500654. short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics 37 (2023) 1548–1565. date_created: 2023-08-01T10:08:32Z date_updated: 2023-08-01T10:09:35Z department: - _id: '542' doi: 10.1137/22m1500654 intvolume: ' 37' issue: '3' keyword: - General Mathematics language: - iso: eng page: 1548-1565 publication: SIAM Journal on Discrete Mathematics publication_identifier: issn: - 0895-4801 - 1095-7146 publication_status: published publisher: Society for Industrial & Applied Mathematics (SIAM) status: public title: Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs type: journal_article user_id: '15540' volume: 37 year: '2023' ... --- _id: '40607' abstract: - lang: eng text: AbstractTeachers’ in-depth diagnostic thinking has been shown to be crucial for student-centered teaching as they need to perceive and interpret students’ understanding for well-informed decision-making on adaptive teaching practices. The paper presents a content-related approach to analyzing diagnostic thinking processes with respect to the mathematical knowledge elements that prospective teachers identify as students’ resources and obstacles. Prospective teachers’ challenge is that some relevant knowledge elements first have to be unpacked, because compact concepts (such as the place value concept) or procedures (such as for multi-digit multiplication) comprise several smaller knowledge elements (such as the positional property) that have to be made explicit for students to foster their learning processes adequately. Our study examines what knowledge elements prospective teachers perceive and interpret in a transcript vignettes on multi-digit multiplication (of decimal and natural numbers) and its underlying basic arithmetic concepts (place value understanding and meaning of multiplication) in written diagnostic judgments on students’ resources and obstacles (N = 196). A comparative design within the vignette is used to investigate how far the process of perceiving can be supported by thematic cues. The analysis reveals that those knowledge elements cued in the vignette by being already unpacked and explicitly addressed are perceived and interpreted more often (but with lower correctness) than those that are uncued and therefore have to be unpacked by the prospective teachers themselves. This confirms the need to prepare prospective teachers for unpacking mathematical concepts themselves. author: - first_name: Jennifer full_name: Dröse, Jennifer last_name: Dröse - first_name: Susanne full_name: Prediger, Susanne last_name: Prediger citation: ama: 'Dröse J, Prediger S. Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements. Journal für Mathematik-Didaktik. Published online 2023. doi:10.1007/s13138-022-00214-w' apa: 'Dröse, J., & Prediger, S. (2023). Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements. Journal Für Mathematik-Didaktik. https://doi.org/10.1007/s13138-022-00214-w' bibtex: '@article{Dröse_Prediger_2023, title={Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements}, DOI={10.1007/s13138-022-00214-w}, journal={Journal für Mathematik-Didaktik}, publisher={Springer Science and Business Media LLC}, author={Dröse, Jennifer and Prediger, Susanne}, year={2023} }' chicago: 'Dröse, Jennifer, and Susanne Prediger. “Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements.” Journal Für Mathematik-Didaktik, 2023. https://doi.org/10.1007/s13138-022-00214-w.' ieee: 'J. Dröse and S. Prediger, “Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements,” Journal für Mathematik-Didaktik, 2023, doi: 10.1007/s13138-022-00214-w.' mla: 'Dröse, Jennifer, and Susanne Prediger. “Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements.” Journal Für Mathematik-Didaktik, Springer Science and Business Media LLC, 2023, doi:10.1007/s13138-022-00214-w.' short: J. Dröse, S. Prediger, Journal Für Mathematik-Didaktik (2023). date_created: 2023-01-27T18:47:24Z date_updated: 2025-01-15T08:36:09Z department: - _id: '98' doi: 10.1007/s13138-022-00214-w keyword: - Education - General Mathematics language: - iso: eng publication: Journal für Mathematik-Didaktik publication_identifier: issn: - 0173-5322 - 1869-2699 publication_status: published publisher: Springer Science and Business Media LLC quality_controlled: '1' status: public title: 'Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements' type: journal_article user_id: '85820' year: '2023' ... --- _id: '50271' author: - first_name: Sevag full_name: Gharibian, Sevag id: '71541' last_name: Gharibian orcid: 0000-0002-9992-3379 - first_name: François full_name: Le Gall, François last_name: Le Gall citation: ama: 'Gharibian S, Le Gall F. Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture. SIAM Journal on Computing. 2023;52(4):1009-1038. doi:10.1137/22m1513721' apa: 'Gharibian, S., & Le Gall, F. (2023). Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture. SIAM Journal on Computing, 52(4), 1009–1038. https://doi.org/10.1137/22m1513721' bibtex: '@article{Gharibian_Le Gall_2023, title={Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture}, volume={52}, DOI={10.1137/22m1513721}, number={4}, journal={SIAM Journal on Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Gharibian, Sevag and Le Gall, François}, year={2023}, pages={1009–1038} }' chicago: 'Gharibian, Sevag, and François Le Gall. “Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture.” SIAM Journal on Computing 52, no. 4 (2023): 1009–38. https://doi.org/10.1137/22m1513721.' ieee: 'S. Gharibian and F. Le Gall, “Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture,” SIAM Journal on Computing, vol. 52, no. 4, pp. 1009–1038, 2023, doi: 10.1137/22m1513721.' mla: 'Gharibian, Sevag, and François Le Gall. “Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture.” SIAM Journal on Computing, vol. 52, no. 4, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 1009–38, doi:10.1137/22m1513721.' short: S. Gharibian, F. Le Gall, SIAM Journal on Computing 52 (2023) 1009–1038. date_created: 2024-01-07T18:19:42Z date_updated: 2026-05-15T08:42:17Z department: - _id: '7' - _id: '623' doi: 10.1137/22m1513721 intvolume: ' 52' issue: '4' keyword: - General Mathematics - General Computer Science language: - iso: eng page: 1009-1038 publication: SIAM Journal on Computing publication_identifier: issn: - 0097-5397 - 1095-7111 publication_status: published publisher: Society for Industrial & Applied Mathematics (SIAM) status: public title: 'Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture' type: journal_article user_id: '71541' volume: 52 year: '2023' ... --- _id: '31982' abstract: - lang: eng text: "AbstractWe show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold

$$\\Sigma $$

\r\n \ Σ\r\n with Betti number

$$b_1$$

\r\n \r\n \ b\r\n 1\r\n \ \r\n , the order of vanishing of the Ruelle zeta function at zero equals

$$4-b_1$$

\r\n \r\n \ 4\r\n -\r\n \ \r\n b\r\n \ 1\r\n \r\n \ \r\n , while in the hyperbolic case it is equal to

$$4-2b_1$$

\r\n \r\n \ 4\r\n -\r\n \ 2\r\n \r\n b\r\n \ 1\r\n \r\n \ \r\n . This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle

$$S\\Sigma $$

\r\n \ \r\n S\r\n Σ\r\n \ \r\n with harmonic 1-forms on

$$\\Sigma $$

\r\n \ Σ\r\n ." author: - first_name: Mihajlo full_name: Cekić, Mihajlo last_name: Cekić - first_name: Benjamin full_name: Delarue, Benjamin id: '70575' last_name: Delarue - first_name: Semyon full_name: Dyatlov, Semyon last_name: Dyatlov - first_name: Gabriel P. full_name: Paternain, Gabriel P. last_name: Paternain citation: ama: Cekić M, Delarue B, Dyatlov S, Paternain GP. The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. Inventiones mathematicae. 2022;229(1):303-394. doi:10.1007/s00222-022-01108-x apa: Cekić, M., Delarue, B., Dyatlov, S., & Paternain, G. P. (2022). The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. Inventiones Mathematicae, 229(1), 303–394. https://doi.org/10.1007/s00222-022-01108-x bibtex: '@article{Cekić_Delarue_Dyatlov_Paternain_2022, title={The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}, volume={229}, DOI={10.1007/s00222-022-01108-x}, number={1}, journal={Inventiones mathematicae}, publisher={Springer Science and Business Media LLC}, author={Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}, year={2022}, pages={303–394} }' chicago: 'Cekić, Mihajlo, Benjamin Delarue, Semyon Dyatlov, and Gabriel P. Paternain. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” Inventiones Mathematicae 229, no. 1 (2022): 303–94. https://doi.org/10.1007/s00222-022-01108-x.' ieee: 'M. Cekić, B. Delarue, S. Dyatlov, and G. P. Paternain, “The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds,” Inventiones mathematicae, vol. 229, no. 1, pp. 303–394, 2022, doi: 10.1007/s00222-022-01108-x.' mla: Cekić, Mihajlo, et al. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” Inventiones Mathematicae, vol. 229, no. 1, Springer Science and Business Media LLC, 2022, pp. 303–94, doi:10.1007/s00222-022-01108-x. short: M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 303–394. date_created: 2022-06-20T08:24:17Z date_updated: 2022-06-21T11:55:15Z department: - _id: '548' doi: 10.1007/s00222-022-01108-x intvolume: ' 229' issue: '1' keyword: - General Mathematics language: - iso: eng page: 303-394 publication: Inventiones mathematicae publication_identifier: issn: - 0020-9910 - 1432-1297 publication_status: published publisher: Springer Science and Business Media LLC status: public title: The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds type: journal_article user_id: '70575' volume: 229 year: '2022' ... --- _id: '34261' abstract: - lang: eng text: Mechanical clinching is used to create lightweight hybrid structures. In order to estimate the service life of clinched components, its fatigue properties need to be known under different mechanical loading conditions. In addition to fatigue, corrosion is another factor that affects the fatigue life of clinched joints. In the literature, many corrosion and high-cycle fatigue damage models exist. However, little is known about how both phenomena interact in clinched joints. In this article, the influence of galvanic corrosion on clinched EN AW-6014/HCT590X + Z sheets on the fatigue life is investigated by means of numerical simulations and experimental results. An accurate prediction of the Wöhler lines of non-corroded and pre-corroded clinched specimens is shown. author: - first_name: Sven full_name: Harzheim, Sven last_name: Harzheim - first_name: Martin full_name: Hofmann, Martin last_name: Hofmann - first_name: Thomas full_name: Wallmersperger, Thomas last_name: Wallmersperger citation: ama: Harzheim S, Hofmann M, Wallmersperger T. Numerical fatigue life prediction of corroded and non-corroded clinched joints. Mechanics of Advanced Materials and Structures. Published online 2022:1-6. doi:10.1080/15376494.2022.2140233 apa: Harzheim, S., Hofmann, M., & Wallmersperger, T. (2022). Numerical fatigue life prediction of corroded and non-corroded clinched joints. Mechanics of Advanced Materials and Structures, 1–6. https://doi.org/10.1080/15376494.2022.2140233 bibtex: '@article{Harzheim_Hofmann_Wallmersperger_2022, title={Numerical fatigue life prediction of corroded and non-corroded clinched joints}, DOI={10.1080/15376494.2022.2140233}, journal={Mechanics of Advanced Materials and Structures}, publisher={Informa UK Limited}, author={Harzheim, Sven and Hofmann, Martin and Wallmersperger, Thomas}, year={2022}, pages={1–6} }' chicago: Harzheim, Sven, Martin Hofmann, and Thomas Wallmersperger. “Numerical Fatigue Life Prediction of Corroded and Non-Corroded Clinched Joints.” Mechanics of Advanced Materials and Structures, 2022, 1–6. https://doi.org/10.1080/15376494.2022.2140233. ieee: 'S. Harzheim, M. Hofmann, and T. Wallmersperger, “Numerical fatigue life prediction of corroded and non-corroded clinched joints,” Mechanics of Advanced Materials and Structures, pp. 1–6, 2022, doi: 10.1080/15376494.2022.2140233.' mla: Harzheim, Sven, et al. “Numerical Fatigue Life Prediction of Corroded and Non-Corroded Clinched Joints.” Mechanics of Advanced Materials and Structures, Informa UK Limited, 2022, pp. 1–6, doi:10.1080/15376494.2022.2140233. short: S. Harzheim, M. Hofmann, T. Wallmersperger, Mechanics of Advanced Materials and Structures (2022) 1–6. date_created: 2022-12-07T10:03:17Z date_updated: 2023-01-02T11:10:49Z department: - _id: '630' doi: 10.1080/15376494.2022.2140233 keyword: - Mechanical Engineering - Mechanics of Materials - General Materials Science - General Mathematics - Civil and Structural Engineering language: - iso: eng page: 1-6 project: - _id: '130' grant_number: '418701707' name: 'TRR 285: TRR 285' - _id: '132' name: 'TRR 285 - B: TRR 285 - Project Area B' - _id: '142' name: 'TRR 285 – B03: TRR 285 - Subproject B03' publication: Mechanics of Advanced Materials and Structures publication_identifier: issn: - 1537-6494 - 1537-6532 publication_status: published publisher: Informa UK Limited status: public title: Numerical fatigue life prediction of corroded and non-corroded clinched joints type: journal_article user_id: '14931' year: '2022' ... --- _id: '35306' author: - first_name: Yannick full_name: Guedes Bonthonneau, Yannick last_name: Guedes Bonthonneau - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Guedes Bonthonneau Y, Weich T. Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. Journal of the European Mathematical Society. 2022;24(3):851-923. doi:10.4171/jems/1103 apa: Guedes Bonthonneau, Y., & Weich, T. (2022). Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. Journal of the European Mathematical Society, 24(3), 851–923. https://doi.org/10.4171/jems/1103 bibtex: '@article{Guedes Bonthonneau_Weich_2022, title={Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}, volume={24}, DOI={10.4171/jems/1103}, number={3}, journal={Journal of the European Mathematical Society}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Guedes Bonthonneau, Yannick and Weich, Tobias}, year={2022}, pages={851–923} }' chicago: 'Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” Journal of the European Mathematical Society 24, no. 3 (2022): 851–923. https://doi.org/10.4171/jems/1103.' ieee: 'Y. Guedes Bonthonneau and T. Weich, “Ruelle–Pollicott resonances for manifolds with hyperbolic cusps,” Journal of the European Mathematical Society, vol. 24, no. 3, pp. 851–923, 2022, doi: 10.4171/jems/1103.' mla: Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” Journal of the European Mathematical Society, vol. 24, no. 3, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 851–923, doi:10.4171/jems/1103. short: Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923. date_created: 2023-01-05T16:23:34Z date_updated: 2023-01-06T08:47:35Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.4171/jems/1103 intvolume: ' 24' issue: '3' keyword: - Applied Mathematics - General Mathematics language: - iso: eng page: 851-923 publication: Journal of the European Mathematical Society publication_identifier: issn: - 1435-9855 publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: Ruelle–Pollicott resonances for manifolds with hyperbolic cusps type: journal_article user_id: '49178' volume: 24 year: '2022' ... --- _id: '45964' abstract: - lang: eng text: "Abstract\r\n Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients in the parabolic equations at a fixed time and utilizing a perturbation argument around the freezed time, it is shown that backward difference time discretizations of linear parabolic equations on an evolving surface along characteristic trajectories can preserve maximal $L^p$-regularity in the discrete setting. The result is applied to prove the stability and convergence of time discretizations of nonlinear parabolic equations on an evolving surface, with linearly implicit backward differentiation formulae characteristic trajectories of the surface, for general locally Lipschitz nonlinearities. The discrete maximal $L^p$-regularity is used to prove the boundedness and stability of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is used to bound the nonlinear terms in the stability analysis. Optimal-order error estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm is obtained by combining the stability analysis with the consistency estimates." author: - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 - first_name: Buyang full_name: Li, Buyang last_name: Li citation: ama: Kovács B, Li B. Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. IMA Journal of Numerical Analysis. Published online 2022. doi:10.1093/imanum/drac033 apa: Kovács, B., & Li, B. (2022). Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac033 bibtex: '@article{Kovács_Li_2022, title={Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems}, DOI={10.1093/imanum/drac033}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }' chicago: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.” IMA Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac033. ieee: 'B. Kovács and B. Li, “Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems,” IMA Journal of Numerical Analysis, 2022, doi: 10.1093/imanum/drac033.' mla: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.” IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2022, doi:10.1093/imanum/drac033. short: B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022). date_created: 2023-07-10T11:45:14Z date_updated: 2024-04-03T09:17:59Z department: - _id: '841' doi: 10.1093/imanum/drac033 keyword: - Applied Mathematics - Computational Mathematics - General Mathematics language: - iso: eng publication: IMA Journal of Numerical Analysis publication_identifier: issn: - 0272-4979 - 1464-3642 publication_status: published publisher: Oxford University Press (OUP) status: public title: Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems type: journal_article user_id: '100441' year: '2022' ... --- _id: '45966' abstract: - lang: eng text: "Abstract\r\n This paper studies bulk–surface splitting methods of first order for (semilinear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a coupled partial differential–algebraic equation system, i.e., the boundary conditions are considered as a second dynamic equation that is coupled to the bulk problem. The splitting approach is combined with bulk–surface finite elements and an implicit Euler discretization of the two subsystems. We prove first-order convergence of the resulting fully discrete scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c h$ for some constant $c>0$. The convergence is also illustrated numerically using dynamic boundary conditions of Allen–Cahn type." author: - first_name: Robert full_name: Altmann, Robert last_name: Altmann - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 - first_name: Christoph full_name: Zimmer, Christoph last_name: Zimmer citation: ama: Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. IMA Journal of Numerical Analysis. 2022;43(2):950-975. doi:10.1093/imanum/drac002 apa: Altmann, R., Kovács, B., & Zimmer, C. (2022). Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. IMA Journal of Numerical Analysis, 43(2), 950–975. https://doi.org/10.1093/imanum/drac002 bibtex: '@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={10.1093/imanum/drac002}, number={2}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022}, pages={950–975} }' chicago: 'Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie Splitting for Parabolic Problems with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis 43, no. 2 (2022): 950–75. https://doi.org/10.1093/imanum/drac002.' ieee: 'R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions,” IMA Journal of Numerical Analysis, vol. 43, no. 2, pp. 950–975, 2022, doi: 10.1093/imanum/drac002.' mla: Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis, vol. 43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:10.1093/imanum/drac002. short: R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022) 950–975. date_created: 2023-07-10T11:45:49Z date_updated: 2024-04-03T09:16:47Z department: - _id: '841' doi: 10.1093/imanum/drac002 intvolume: ' 43' issue: '2' keyword: - Applied Mathematics - Computational Mathematics - General Mathematics language: - iso: eng page: 950-975 publication: IMA Journal of Numerical Analysis publication_identifier: issn: - 0272-4979 - 1464-3642 publication_status: published publisher: Oxford University Press (OUP) status: public title: Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions type: journal_article user_id: '100441' volume: 43 year: '2022' ... --- _id: '45968' abstract: - lang: eng text: "Abstract\r\n We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe the coupling and the dynamics in the abstract bulk- and surface-spaces, and treats the nonlinear terms similarly to an exponential integrator. The convergence proof is based on estimates for a recursive formulation of the error, using the parabolic smoothing property of analytic semigroups, and a careful comparison of the exact and approximate flows. This analysis also requires a deep understanding of the effects of the Dirichlet operator (the abstract version of the harmonic extension operator), which is essential for the stable coupling in our method. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented." author: - first_name: Petra full_name: Csomós, Petra last_name: Csomós - first_name: Bálint full_name: Farkas, Bálint last_name: Farkas - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 citation: ama: Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. IMA Journal of Numerical Analysis. Published online 2022. doi:10.1093/imanum/drac079 apa: Csomós, P., Farkas, B., & Kovács, B. (2022). Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac079 bibtex: '@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting integrator for abstract semilinear boundary coupled systems}, DOI={10.1093/imanum/drac079}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022} }' chicago: Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” IMA Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac079. ieee: 'P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator for abstract semilinear boundary coupled systems,” IMA Journal of Numerical Analysis, 2022, doi: 10.1093/imanum/drac079.' mla: Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2022, doi:10.1093/imanum/drac079. short: P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022). date_created: 2023-07-10T11:46:54Z date_updated: 2024-04-03T09:15:52Z department: - _id: '841' doi: 10.1093/imanum/drac079 keyword: - Applied Mathematics - Computational Mathematics - General Mathematics language: - iso: eng publication: IMA Journal of Numerical Analysis publication_identifier: issn: - 0272-4979 - 1464-3642 publication_status: published publisher: Oxford University Press (OUP) status: public title: Error estimates for a splitting integrator for abstract semilinear boundary coupled systems type: journal_article user_id: '100441' year: '2022' ... --- _id: '53319' abstract: - lang: eng text: "Abstract\r\n The Neumann problem for (0.1)$$ \\begin{align}& V_t = \\Delta V-aV+f(x,t) \\end{align}$$is considered in bounded domains $\\Omega \\subset {\\mathbb {R}}^n$ with smooth boundary, where $n\\ge 1$ and $a\\in {\\mathbb {R}}$. By means of a variational approach, a statement on boundedness of the quantities $$ \\begin{eqnarray*} \\sup_{t\\in (0,T)} \\int_\\Omega \\big|\\nabla V(\\cdot,t)\\big|^p L^{\\frac{n+p}{n+2}} \\Big( \\big|\\nabla V(\\cdot,t)\\big| \\Big) \\end{eqnarray*}$$in dependence on the expressions (0.2)$$ \\begin{align}& \\sup_{t\\in (0,T-\\tau)} \\int_t^{t+\\tau} \\int_\\Omega |f|^{\\frac{(n+2)p}{n+p}} L\\big( |f|\\big) \\end{align}$$is derived for $p\\ge 2$, $\\tau>0$, and $T\\ge 2\\tau $, provided that $L\\in C^0([0,\\infty ))$ is positive, strictly increasing, unbounded, and slowly growing in the sense that $\\limsup _{s\\to \\infty } \\frac {L(s^{\\lambda _0})}{L(s)} <\\infty $ for some $\\lambda _0>1$. In the particular case when $p=n\\ge 2$, an additional condition on growth of $L$, particularly satisfied by $L(\\xi ):=\\ln ^\\alpha (\\xi +b)$ whenever $b>0$ and $\\alpha>\\frac {(n+2)(n-1)}{2n}$, is identified as sufficient to ensure that as a consequence of the above, bounds for theintegrals in (0.2) even imply estimates for the spatio-temporal modulus of continuity of solutions to (0.1). A subsequent application to the Keller–Segel system $$ \\begin{eqnarray*} \\left\\{ \\begin{array}{l} u_t = \\nabla \\cdot \\big( D(v)\\nabla u\\big) - \\nabla \\cdot \\big( uS(v)\\nabla v\\big) + ru - \\mu u^2, \\\\[1mm] v_t = \\Delta v-v+u, \\end{array} \\right. \\end{eqnarray*}$$shows that when $n=2$, $r\\in {\\mathbb {R}}$, $0<D\\in C^2([0,\\infty ))$, and $S\\in C^2([0,\\infty )) \\cap W^{1,\\infty }((0,\\infty ))$ and thus especially in the presence of arbitrarily strong diffusion degeneracies implied by rapid decay of $D$, any choice of $\\mu>0$ excludes blowup in the sense that for all suitably regular nonnegative initial data, an associated initial-boundary value problem admits a global bounded classical solution." author: - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Winkler M. A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System. International Mathematics Research Notices. 2022;2023(19):16336-16393. doi:10.1093/imrn/rnac286 apa: Winkler, M. (2022). A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System. International Mathematics Research Notices, 2023(19), 16336–16393. https://doi.org/10.1093/imrn/rnac286 bibtex: '@article{Winkler_2022, title={A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System}, volume={2023}, DOI={10.1093/imrn/rnac286}, number={19}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Winkler, Michael}, year={2022}, pages={16336–16393} }' chicago: 'Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System.” International Mathematics Research Notices 2023, no. 19 (2022): 16336–93. https://doi.org/10.1093/imrn/rnac286.' ieee: 'M. Winkler, “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System,” International Mathematics Research Notices, vol. 2023, no. 19, pp. 16336–16393, 2022, doi: 10.1093/imrn/rnac286.' mla: Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System.” International Mathematics Research Notices, vol. 2023, no. 19, Oxford University Press (OUP), 2022, pp. 16336–93, doi:10.1093/imrn/rnac286. short: M. Winkler, International Mathematics Research Notices 2023 (2022) 16336–16393. date_created: 2024-04-07T12:33:44Z date_updated: 2024-04-07T12:36:06Z doi: 10.1093/imrn/rnac286 intvolume: ' 2023' issue: '19' keyword: - General Mathematics language: - iso: eng page: 16336-16393 publication: International Mathematics Research Notices publication_identifier: issn: - 1073-7928 - 1687-0247 publication_status: published publisher: Oxford University Press (OUP) status: public title: A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System type: journal_article user_id: '31496' volume: 2023 year: '2022' ... --- _id: '53321' abstract: - lang: eng text: ' The chemotaxis system [Formula: see text] is considered in a ball [Formula: see text], [Formula: see text], where the positive function [Formula: see text] reflects suitably weak diffusion by satisfying [Formula: see text] for some [Formula: see text]. It is shown that whenever [Formula: see text] is positive and satisfies [Formula: see text] as [Formula: see text], one can find a suitably regular nonlinearity [Formula: see text] with the property that at each sufficiently large mass level [Formula: see text] there exists a globally defined radially symmetric classical solution to a Neumann-type boundary value problem for (⋆) which satisfies [Formula: see text] ' author: - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Winkler M. Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems. Communications in Contemporary Mathematics. 2022;25(10). doi:10.1142/s0219199722500626 apa: Winkler, M. (2022). Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems. Communications in Contemporary Mathematics, 25(10). https://doi.org/10.1142/s0219199722500626 bibtex: '@article{Winkler_2022, title={Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems}, volume={25}, DOI={10.1142/s0219199722500626}, number={10}, journal={Communications in Contemporary Mathematics}, publisher={World Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }' chicago: Winkler, Michael. “Arbitrarily Fast Grow-up Rates in Quasilinear Keller–Segel Systems.” Communications in Contemporary Mathematics 25, no. 10 (2022). https://doi.org/10.1142/s0219199722500626. ieee: 'M. Winkler, “Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems,” Communications in Contemporary Mathematics, vol. 25, no. 10, 2022, doi: 10.1142/s0219199722500626.' mla: Winkler, Michael. “Arbitrarily Fast Grow-up Rates in Quasilinear Keller–Segel Systems.” Communications in Contemporary Mathematics, vol. 25, no. 10, World Scientific Pub Co Pte Ltd, 2022, doi:10.1142/s0219199722500626. short: M. Winkler, Communications in Contemporary Mathematics 25 (2022). date_created: 2024-04-07T12:35:09Z date_updated: 2024-04-07T12:35:53Z doi: 10.1142/s0219199722500626 intvolume: ' 25' issue: '10' keyword: - Applied Mathematics - General Mathematics language: - iso: eng publication: Communications in Contemporary Mathematics publication_identifier: issn: - 0219-1997 - 1793-6683 publication_status: published publisher: World Scientific Pub Co Pte Ltd status: public title: Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems type: journal_article user_id: '31496' volume: 25 year: '2022' ...