[{"keyword":["General Mathematics"],"type":"journal_article","date_created":"2024-04-07T12:27:28Z","abstract":[{"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.","lang":"eng"}],"issue":"3","publication":"Journal of the London Mathematical Society","doi":"10.1112/jlms.12885","language":[{"iso":"eng"}],"intvolume":" 109","date_updated":"2024-04-07T12:36:25Z","publication_status":"published","publication_identifier":{"issn":["0024-6107","1469-7750"]},"author":[{"full_name":"Wang, Yulan","last_name":"Wang","first_name":"Yulan"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"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","year":"2024","citation":{"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.","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","short":"Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (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.","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.","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} }","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"},"volume":109,"user_id":"31496","_id":"53315","publisher":"Wiley","status":"public"},{"author":[{"full_name":"Bartels, Sören","last_name":"Bartels","first_name":"Sören"},{"full_name":"Kovács, Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs","id":"100441"},{"last_name":"Wang","first_name":"Zhangxian","full_name":"Wang, Zhangxian"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"year":"2023","status":"public","title":"Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints","publication_status":"published","date_updated":"2024-04-03T09:15:27Z","publisher":"Oxford University Press (OUP)","_id":"45971","language":[{"iso":"eng"}],"user_id":"100441","doi":"10.1093/imanum/drad037","citation":{"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.","short":"S. Bartels, B. Kovács, Z. Wang, IMA Journal of Numerical Analysis (2023).","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","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.","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","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} }","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."},"publication":"IMA Journal of Numerical Analysis","abstract":[{"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.","lang":"eng"}],"date_created":"2023-07-10T12:32:10Z","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article"},{"date_created":"2024-04-07T12:41:49Z","keyword":["Applied Mathematics","General Mathematics"],"type":"journal_article","publication":"Communications in Mathematical Sciences","issue":"2","language":[{"iso":"eng"}],"doi":"10.4310/cms.2023.v21.n2.a1","publication_identifier":{"issn":["1539-6746","1945-0796"]},"author":[{"last_name":"Li","first_name":"Genglin","full_name":"Li, Genglin"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"title":"Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities","year":"2023","intvolume":" 21","publication_status":"published","date_updated":"2024-04-07T12:41:54Z","citation":{"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.","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","bibtex":"@article{Li_Winkler_2023, title={Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities}, volume={21}, DOI={10.4310/cms.2023.v21.n2.a1}, number={2}, journal={Communications in Mathematical Sciences}, publisher={International Press of Boston}, author={Li, Genglin and Winkler, Michael}, year={2023}, pages={299–322} }","apa":"Li, G., & Winkler, M. (2023). Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Communications in Mathematical Sciences, 21(2), 299–322. https://doi.org/10.4310/cms.2023.v21.n2.a1","ieee":"G. Li and M. Winkler, “Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities,” Communications in Mathematical Sciences, vol. 21, no. 2, pp. 299–322, 2023, doi: 10.4310/cms.2023.v21.n2.a1.","chicago":"Li, Genglin, and Michael Winkler. “Relaxation in a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Communications in Mathematical Sciences 21, no. 2 (2023): 299–322. https://doi.org/10.4310/cms.2023.v21.n2.a1.","short":"G. Li, M. Winkler, Communications in Mathematical Sciences 21 (2023) 299–322."},"_id":"53326","publisher":"International Press of Boston","page":"299-322","volume":21,"user_id":"31496","status":"public"},{"_id":"53343","publisher":"Walter de Gruyter GmbH","volume":21,"user_id":"31496","status":"public","citation":{"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.","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","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.","short":"M. Winkler, Open Mathematics 21 (2023).","mla":"Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” Open Mathematics, vol. 21, no. 1, Walter de Gruyter GmbH, 2023, doi:10.1515/math-2022-0578.","bibtex":"@article{Winkler_2023, title={Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type}, volume={21}, DOI={10.1515/math-2022-0578}, number={1}, journal={Open Mathematics}, publisher={Walter de Gruyter GmbH}, author={Winkler, Michael}, year={2023} }","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"},"language":[{"iso":"eng"}],"doi":"10.1515/math-2022-0578","publication_identifier":{"issn":["2391-5455"]},"author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"year":"2023","title":"Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type","intvolume":" 21","publication_status":"published","date_updated":"2024-04-07T12:54:34Z","date_created":"2024-04-07T12:54:31Z","keyword":["General Mathematics"],"type":"journal_article","publication":"Open Mathematics","issue":"1","abstract":[{"text":"Abstract\r\n The Cauchy problem in \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n {{\\mathbb{R}}}^{n}\r\n \r\n , \r\n \r\n \r\n \r\n n\r\n ≥\r\n 2\r\n \r\n n\\ge 2\r\n \r\n , for \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n \r\n \r\n t\r\n \r\n \r\n =\r\n Δ\r\n u\r\n −\r\n \r\n ∇\r\n \r\n ⋅\r\n \r\n (\r\n \r\n u\r\n S\r\n ⋅\r\n \r\n ∇\r\n \r\n v\r\n \r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n +\r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n (\r\n \r\n ⋆\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n \\begin{array}{r}\\left\\{\\phantom{\\rule[-1.25em]{}{0ex}}\\begin{array}{l}{u}_{t}=\\Delta u-\\nabla \\cdot \\left(uS\\cdot \\nabla v),\\\\ 0=\\Delta v+u,\\end{array}\\right.\\hspace{2.0em}\\hspace{2.0em}\\hspace{2.0em}\\left(\\star )\\end{array}\r\n \r\n is considered for general matrices \r\n \r\n \r\n \r\n S\r\n ∈\r\n \r\n \r\n R\r\n \r\n \r\n n\r\n ×\r\n n\r\n \r\n \r\n \r\n S\\in {{\\mathbb{R}}}^{n\\times n}\r\n \r\n . A theory of local-in-time classical existence and extensibility is developed in a framework that differs from those considered in large parts of the literature by involving bounded classical solutions. Specifically, it is shown that for all non-negative initial data belonging to \r\n \r\n \r\n \r\n BUC\r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n ∩\r\n \r\n \r\n L\r\n \r\n \r\n p\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n {\\rm{BUC}}\\left({{\\mathbb{R}}}^{n})\\cap {L}^{p}\\left({{\\mathbb{R}}}^{n})\r\n \r\n with some \r\n \r\n \r\n \r\n p\r\n ∈\r\n \r\n [\r\n \r\n 1\r\n ,\r\n n\r\n \r\n )\r\n \r\n \r\n p\\in \\left[1,n)\r\n \r\n , there exist \r\n \r\n \r\n \r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n ∈\r\n \r\n (\r\n \r\n 0\r\n ,\r\n ∞\r\n \r\n ]\r\n \r\n \r\n {T}_{\\max }\\in \\left(0,\\infty ]\r\n \r\n and a uniquely determined \r\n \r\n \r\n \r\n u\r\n ∈\r\n \r\n \r\n C\r\n \r\n \r\n 0\r\n \r\n \r\n \r\n (\r\n \r\n \r\n [\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n ;\r\n \r\n BUC\r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n )\r\n \r\n ∩\r\n \r\n \r\n C\r\n \r\n \r\n 0\r\n \r\n \r\n \r\n (\r\n \r\n \r\n [\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n ;\r\n \r\n \r\n \r\n L\r\n \r\n \r\n p\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n )\r\n \r\n ∩\r\n \r\n \r\n C\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n ×\r\n \r\n (\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n \r\n )\r\n \r\n \r\n u\\in {C}^{0}\\left(\\left[0,{T}_{\\max });\\hspace{0.33em}{\\rm{BUC}}\\left({{\\mathbb{R}}}^{n}))\\cap {C}^{0}\\left(\\left[0,{T}_{\\max });\\hspace{0.33em}{L}^{p}\\left({{\\mathbb{R}}}^{n}))\\cap {C}^{\\infty }\\left({{\\mathbb{R}}}^{n}\\times \\left(0,{T}_{\\max }))\r\n \r\n such that with \r\n \r\n \r\n \r\n v\r\n ≔\r\n Γ\r\n ⋆\r\n u\r\n \r\n v:= \\Gamma \\star u\r\n \r\n , and with \r\n \r\n \r\n \r\n Γ\r\n \r\n \\Gamma \r\n \r\n denoting the Newtonian kernel on \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n {{\\mathbb{R}}}^{n}\r\n \r\n , the pair \r\n \r\n \r\n \r\n \r\n (\r\n \r\n u\r\n ,\r\n v\r\n \r\n )\r\n \r\n \r\n \\left(u,v)\r\n \r\n forms a classical solution of (\r\n \r\n \r\n \r\n ⋆\r\n \r\n \\star \r\n \r\n ) in \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n ×\r\n \r\n (\r\n \r\n 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n \r\n {{\\mathbb{R}}}^{n}\\times \\left(0,{T}_{\\max })\r\n \r\n , which has the property that \r\n \r\n \r\n \r\n \r\n if\r\n \r\n \r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n <\r\n ∞\r\n ,\r\n \r\n \r\n \r\n then both\r\n \r\n \r\n \r\n \r\n \r\n limsup\r\n \r\n \r\n t\r\n ↗\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n \r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n \r\n ⋅\r\n ,\r\n t\r\n \r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n \r\n L\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n \r\n =\r\n ∞\r\n \r\n \r\n and\r\n \r\n \r\n \r\n \r\n limsup\r\n \r\n \r\n t\r\n ↗\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n \r\n \r\n \r\n ‖\r\n \r\n ∇\r\n \r\n v\r\n \r\n (\r\n \r\n ⋅\r\n ,\r\n t\r\n \r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n \r\n L\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n \r\n =\r\n ∞\r\n .\r\n \r\n \\hspace{0.1em}\\text{if}\\hspace{0.1em}\\hspace{0.33em}{T}_{\\max }\\lt \\infty ,\\hspace{1.0em}\\hspace{0.1em}\\text{then both}\\hspace{0.1em}\\hspace{0.33em}\\mathop{\\mathrm{limsup}}\\limits_{t\\nearrow {T}_{\\max }}\\Vert u\\left(\\cdot ,t){\\Vert }_{{L}^{\\infty }\\left({{\\mathbb{R}}}^{n})}=\\infty \\hspace{1.0em}\\hspace{0.1em}\\text{and}\\hspace{0.1em}\\hspace{1.0em}\\mathop{\\mathrm{limsup}}\\limits_{t\\nearrow {T}_{\\max }}\\Vert \\nabla v\\left(\\cdot ,t){\\Vert }_{{L}^{\\infty }\\left({{\\mathbb{R}}}^{n})}=\\infty .\r\n \r\n An exemplary application of this provides a result on global classical solvability in cases when \r\n \r\n \r\n \r\n ∣\r\n S\r\n +\r\n 1\r\n ∣\r\n \r\n | S+{\\bf{1}}| \r\n \r\n is sufficiently small, where \r\n \r\n \r\n \r\n 1\r\n =\r\n diag\r\n \r\n \r\n (\r\n \r\n 1\r\n ,\r\n \r\n …\r\n \r\n ,\r\n 1\r\n \r\n )\r\n \r\n \r\n {\\bf{1}}={\\rm{diag}}\\hspace{0.33em}\\left(1,\\ldots ,1)\r\n \r\n .","lang":"eng"}]},{"intvolume":" 46","publication_status":"published","date_updated":"2024-04-07T12:51:31Z","publication_identifier":{"issn":["0170-4214","1099-1476"]},"author":[{"first_name":"Yu","last_name":"Tian","full_name":"Tian, Yu"},{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"title":"Keller–Segel–Stokes interaction involving signal‐dependent motilities","year":"2023","doi":"10.1002/mma.9419","language":[{"iso":"eng"}],"abstract":[{"text":"The chemotaxis‐Stokes system \r\n\r\n\r\nis considered along with homogeneous boundary conditions of no‐flux type for \r\n and \r\n, and of Dirichlet type for \r\n, in a smoothly bounded domain \r\n. Under the assumption that \r\n, that \r\n is bounded on each of the intervals \r\n with arbitrary \r\n, and that with some \r\n and \r\n, we have \r\n\r\n\r\nIt is shown that for any suitably regular initial data, an associated initial‐boundary value problem admits a global very weak solution.","lang":"eng"}],"publication":"Mathematical Methods in the Applied Sciences","issue":"14","type":"journal_article","keyword":["General Engineering","General Mathematics"],"date_created":"2024-04-07T12:51:27Z","status":"public","volume":46,"user_id":"31496","_id":"53339","publisher":"Wiley","page":"15667-15683","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","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} }","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.","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.","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","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."}},{"_id":"53538","language":[{"iso":"eng"}],"publisher":"Springer Science and Business Media LLC","doi":"10.1007/s13163-023-00476-z","user_id":"100325","year":"2023","status":"public","title":"New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation","author":[{"full_name":"Polychrou, G.","last_name":"Polychrou","first_name":"G."},{"id":"100325","full_name":"Papageorgiou, Efthymia","last_name":"Papageorgiou","first_name":"Efthymia"},{"full_name":"Fotiadis, A.","first_name":"A.","last_name":"Fotiadis"},{"full_name":"Daskaloyannis, C.","last_name":"Daskaloyannis","first_name":"C."}],"publication_identifier":{"issn":["1139-1138","1988-2807"]},"date_updated":"2024-04-17T13:15:51Z","publication_status":"published","date_created":"2024-04-17T13:15:07Z","keyword":["General Mathematics"],"type":"journal_article","department":[{"_id":"555"}],"publication":"Revista Matemática Complutense","citation":{"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","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.","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.","short":"G. Polychrou, E. Papageorgiou, A. Fotiadis, C. Daskaloyannis, Revista Matemática Complutense (2023).","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.","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","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} }"},"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."}]},{"file":[{"access_level":"closed","file_size":1460246,"file_name":"s11858-023-01505-3.pdf","date_updated":"2023-07-13T09:40:02Z","relation":"main_file","content_type":"application/pdf","success":1,"file_id":"46041","creator":"maxh","date_created":"2023-07-13T09:40:02Z"}],"date_created":"2023-06-27T11:45:25Z","type":"journal_article","keyword":["General Mathematics","Education"],"department":[{"_id":"643"}],"publication":"ZDM – Mathematics Education","abstract":[{"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.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/s11858-023-01505-3"}],"language":[{"iso":"eng"}],"doi":"10.1007/s11858-023-01505-3","year":"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","publication_identifier":{"issn":["1863-9690","1863-9704"]},"author":[{"full_name":"Hoffmann, Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","first_name":"Max","id":"32202"},{"id":"16274","last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf"}],"publication_status":"published","date_updated":"2024-04-18T09:01:29Z","article_type":"original","oa":"1","file_date_updated":"2023-07-13T09:40:02Z","citation":{"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} }","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","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).","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.","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"},"quality_controlled":"1","_id":"45786","publisher":"Springer","user_id":"37888","ddc":["510","370"],"status":"public","has_accepted_license":"1"},{"date_created":"2023-08-17T10:11:45Z","type":"journal_article","keyword":["General Mathematics","Education"],"department":[{"_id":"913"}],"publication":"ZDM – Mathematics Education","citation":{"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","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.","short":"J. Schoenherr, S. Schukajlow, ZDM – Mathematics Education (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.","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.","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","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} }"},"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."}],"_id":"46569","language":[{"iso":"eng"}],"publisher":"Springer Science and Business Media LLC","doi":"10.1007/s11858-023-01494-3","user_id":"99409","year":"2023","status":"public","title":"Characterizing external visualization in mathematics education research: a scoping review","publication_identifier":{"issn":["1863-9690","1863-9704"]},"author":[{"full_name":"Schoenherr, Johanna","last_name":"Schoenherr","first_name":"Johanna"},{"first_name":"Stanislaw","last_name":"Schukajlow","full_name":"Schukajlow, Stanislaw"}],"date_updated":"2024-04-30T13:43:22Z","publication_status":"published"},{"citation":{"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.","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} }","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","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.","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","short":"A. Ernst, K.-U. Schmidt, Mathematical Proceedings of the Cambridge Philosophical Society 175 (2023) 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."},"publisher":"Cambridge University Press (CUP)","_id":"53533","page":"129-160","volume":175,"user_id":"46953","status":"public","date_created":"2024-04-17T12:23:18Z","department":[{"_id":"100"}],"keyword":["General Mathematics"],"type":"journal_article","issue":"1","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","language":[{"iso":"eng"}],"doi":"10.1017/s0305004123000075","publication_identifier":{"issn":["0305-0041","1469-8064"]},"author":[{"id":"46953","full_name":"Ernst, Alena","last_name":"Ernst","first_name":"Alena"},{"first_name":"Kai-Uwe","last_name":"Schmidt","full_name":"Schmidt, Kai-Uwe"}],"title":"Intersection theorems for finite general linear groups","year":"2023","intvolume":" 175","publication_status":"published","date_updated":"2024-05-07T08:29:59Z"},{"publication_status":"published","date_updated":"2023-08-01T10:09:35Z","intvolume":" 37","year":"2023","title":"Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs","publication_identifier":{"issn":["0895-4801","1095-7146"]},"author":[{"first_name":"Yulai","last_name":"Ma","full_name":"Ma, Yulai","id":"92748"},{"full_name":"Mattiolo, Davide","last_name":"Mattiolo","first_name":"Davide"},{"id":"15548","full_name":"Steffen, Eckhard","last_name":"Steffen","first_name":"Eckhard","orcid":"0000-0002-9808-7401"},{"id":"88145","full_name":"Wolf, Isaak Hieronymus","last_name":"Wolf","first_name":"Isaak Hieronymus"}],"doi":"10.1137/22m1500654","language":[{"iso":"eng"}],"issue":"3","publication":"SIAM Journal on Discrete Mathematics","type":"journal_article","keyword":["General Mathematics"],"department":[{"_id":"542"}],"date_created":"2023-08-01T10:08:32Z","status":"public","user_id":"15540","volume":37,"page":"1548-1565","_id":"46256","publisher":"Society for Industrial & Applied Mathematics (SIAM)","citation":{"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.","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","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} }","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","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.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics 37 (2023) 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."}},{"type":"journal_article","keyword":["Education","General Mathematics"],"department":[{"_id":"98"}],"date_created":"2023-01-27T18:47:24Z","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","publication":"Journal für Mathematik-Didaktik","citation":{"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","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.","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.","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.","short":"J. Dröse, S. Prediger, Journal Für Mathematik-Didaktik (2023).","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","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} }"},"doi":"10.1007/s13138-022-00214-w","user_id":"85820","publisher":"Springer Science and Business Media LLC","_id":"40607","language":[{"iso":"eng"}],"date_updated":"2025-01-15T08:36:09Z","publication_status":"published","title":"Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements","status":"public","year":"2023","author":[{"full_name":"Dröse, Jennifer","first_name":"Jennifer","last_name":"Dröse"},{"last_name":"Prediger","first_name":"Susanne","full_name":"Prediger, Susanne"}],"publication_identifier":{"issn":["0173-5322","1869-2699"]}},{"citation":{"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.","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} }","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","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.","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","short":"S. Gharibian, F. Le Gall, SIAM Journal on Computing 52 (2023) 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."},"publisher":"Society for Industrial & Applied Mathematics (SIAM)","_id":"50271","page":"1009-1038","volume":52,"user_id":"71541","status":"public","date_created":"2024-01-07T18:19:42Z","department":[{"_id":"7"},{"_id":"623"}],"keyword":["General Mathematics","General Computer Science"],"type":"journal_article","issue":"4","publication":"SIAM Journal on Computing","language":[{"iso":"eng"}],"doi":"10.1137/22m1513721","author":[{"full_name":"Gharibian, Sevag","orcid":"0000-0002-9992-3379","first_name":"Sevag","last_name":"Gharibian","id":"71541"},{"last_name":"Le Gall","first_name":"François","full_name":"Le Gall, François"}],"publication_identifier":{"issn":["0097-5397","1095-7111"]},"year":"2023","title":"Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture","intvolume":" 52","date_updated":"2026-05-15T08:42:17Z","publication_status":"published"},{"date_created":"2022-06-20T08:24:17Z","department":[{"_id":"548"}],"keyword":["General Mathematics"],"type":"journal_article","publication":"Inventiones mathematicae","issue":"1","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 ."}],"language":[{"iso":"eng"}],"doi":"10.1007/s00222-022-01108-x","publication_identifier":{"issn":["0020-9910","1432-1297"]},"author":[{"full_name":"Cekić, Mihajlo","first_name":"Mihajlo","last_name":"Cekić"},{"full_name":"Delarue, Benjamin","first_name":"Benjamin","last_name":"Delarue","id":"70575"},{"full_name":"Dyatlov, Semyon","last_name":"Dyatlov","first_name":"Semyon"},{"full_name":"Paternain, Gabriel P.","last_name":"Paternain","first_name":"Gabriel P."}],"year":"2022","title":"The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds","intvolume":" 229","publication_status":"published","date_updated":"2022-06-21T11:55:15Z","citation":{"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.","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","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} }","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","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.","short":"M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 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."},"_id":"31982","publisher":"Springer Science and Business Media LLC","page":"303-394","volume":229,"user_id":"70575","status":"public"},{"status":"public","page":"1-6","_id":"34261","publisher":"Informa UK Limited","user_id":"14931","citation":{"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.","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","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} }","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","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.","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.","short":"S. Harzheim, M. Hofmann, T. Wallmersperger, Mechanics of Advanced Materials and Structures (2022) 1–6."},"project":[{"name":"TRR 285: TRR 285","grant_number":"418701707","_id":"130"},{"_id":"132","name":"TRR 285 - B: TRR 285 - Project Area B"},{"_id":"142","name":"TRR 285 – B03: TRR 285 - Subproject B03"}],"title":"Numerical fatigue life prediction of corroded and non-corroded clinched joints","year":"2022","publication_identifier":{"issn":["1537-6494","1537-6532"]},"author":[{"last_name":"Harzheim","first_name":"Sven","full_name":"Harzheim, Sven"},{"full_name":"Hofmann, Martin","first_name":"Martin","last_name":"Hofmann"},{"last_name":"Wallmersperger","first_name":"Thomas","full_name":"Wallmersperger, Thomas"}],"publication_status":"published","date_updated":"2023-01-02T11:10:49Z","language":[{"iso":"eng"}],"doi":"10.1080/15376494.2022.2140233","publication":"Mechanics of Advanced Materials and Structures","abstract":[{"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.","lang":"eng"}],"date_created":"2022-12-07T10:03:17Z","keyword":["Mechanical Engineering","Mechanics of Materials","General Materials Science","General Mathematics","Civil and Structural Engineering"],"type":"journal_article","department":[{"_id":"630"}]},{"title":"Ruelle–Pollicott resonances for manifolds with hyperbolic cusps","year":"2022","author":[{"full_name":"Guedes Bonthonneau, Yannick","first_name":"Yannick","last_name":"Guedes Bonthonneau"},{"id":"49178","last_name":"Weich","first_name":"Tobias","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias"}],"publication_identifier":{"issn":["1435-9855"]},"date_updated":"2023-01-06T08:47:35Z","publication_status":"published","intvolume":" 24","language":[{"iso":"eng"}],"doi":"10.4171/jems/1103","publication":"Journal of the European Mathematical Society","issue":"3","date_created":"2023-01-05T16:23:34Z","keyword":["Applied Mathematics","General Mathematics"],"type":"journal_article","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"status":"public","page":"851-923","_id":"35306","publisher":"European Mathematical Society - EMS - Publishing House GmbH","user_id":"49178","volume":24,"citation":{"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.","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","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.","short":"Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923.","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.","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} }","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"}},{"publication":"IMA Journal of Numerical Analysis","citation":{"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","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.","short":"B. Kovács, B. Li, IMA Journal of Numerical Analysis (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.","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.","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","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} }"},"abstract":[{"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.","lang":"eng"}],"date_created":"2023-07-10T11:45:14Z","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","department":[{"_id":"841"}],"status":"public","year":"2022","title":"Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems","author":[{"id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs","full_name":"Kovács, Balázs"},{"full_name":"Li, Buyang","first_name":"Buyang","last_name":"Li"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"date_updated":"2024-04-03T09:17:59Z","publication_status":"published","_id":"45964","publisher":"Oxford University Press (OUP)","language":[{"iso":"eng"}],"doi":"10.1093/imanum/drac033","user_id":"100441"},{"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","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} }","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.","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.","short":"R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022) 950–975.","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","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."},"volume":43,"user_id":"100441","publisher":"Oxford University Press (OUP)","_id":"45966","page":"950-975","status":"public","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","date_created":"2023-07-10T11:45:49Z","abstract":[{"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 $c&gt;0$. The convergence is also illustrated numerically using dynamic boundary conditions of Allen–Cahn type.","lang":"eng"}],"publication":"IMA Journal of Numerical Analysis","issue":"2","doi":"10.1093/imanum/drac002","language":[{"iso":"eng"}],"intvolume":" 43","publication_status":"published","date_updated":"2024-04-03T09:16:47Z","publication_identifier":{"issn":["0272-4979","1464-3642"]},"author":[{"last_name":"Altmann","first_name":"Robert","full_name":"Altmann, Robert"},{"full_name":"Kovács, Balázs","first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","id":"100441"},{"last_name":"Zimmer","first_name":"Christoph","full_name":"Zimmer, Christoph"}],"title":"Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions","year":"2022"},{"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."}],"publication":"IMA Journal of Numerical Analysis","citation":{"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} }","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","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).","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.","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"},"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"department":[{"_id":"841"}],"date_created":"2023-07-10T11:46:54Z","publication_status":"published","date_updated":"2024-04-03T09:15:52Z","status":"public","title":"Error estimates for a splitting integrator for abstract semilinear boundary coupled systems","year":"2022","author":[{"full_name":"Csomós, Petra","last_name":"Csomós","first_name":"Petra"},{"full_name":"Farkas, Bálint","first_name":"Bálint","last_name":"Farkas"},{"id":"100441","last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"user_id":"100441","doi":"10.1093/imanum/drac079","language":[{"iso":"eng"}],"_id":"45968","publisher":"Oxford University Press (OUP)"},{"publication_identifier":{"issn":["1073-7928","1687-0247"]},"author":[{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"year":"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","intvolume":" 2023","publication_status":"published","date_updated":"2024-04-07T12:36:06Z","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rnac286","issue":"19","publication":"International Mathematics Research Notices","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 $p\\ge 2$, $\\tau&gt;0$, 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)} &lt;\\infty $ for some $\\lambda _0&gt;1$. 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 $b&gt;0$ and $\\alpha&gt;\\frac {(n+2)(n-1)}{2n}$, 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 $n=2$, $r\\in {\\mathbb {R}}$, $0&lt;D\\in C^2([0,\\infty ))$, 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 $\\mu&gt;0$ 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."}],"date_created":"2024-04-07T12:33:44Z","type":"journal_article","keyword":["General Mathematics"],"status":"public","publisher":"Oxford University Press (OUP)","_id":"53319","page":"16336-16393","volume":2023,"user_id":"31496","citation":{"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.","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","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} }","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","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.","short":"M. Winkler, International Mathematics Research Notices 2023 (2022) 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."}},{"citation":{"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.","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} }","ama":"Winkler M. Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems. Communications in Contemporary Mathematics. 2022;25(10). doi: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.","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","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.","short":"M. Winkler, Communications in Contemporary Mathematics 25 (2022)."},"status":"public","user_id":"31496","volume":25,"publisher":"World Scientific Pub Co Pte Ltd","_id":"53321","abstract":[{"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] ","lang":"eng"}],"publication":"Communications in Contemporary Mathematics","issue":"10","keyword":["Applied Mathematics","General Mathematics"],"type":"journal_article","date_created":"2024-04-07T12:35:09Z","date_updated":"2024-04-07T12:35:53Z","publication_status":"published","intvolume":" 25","title":"Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems","year":"2022","author":[{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"publication_identifier":{"issn":["0219-1997","1793-6683"]},"doi":"10.1142/s0219199722500626","language":[{"iso":"eng"}]}]