[{"user_id":"31496","_id":"53331","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"publication":"Proceedings of the Royal Society of Edinburgh: Section A Mathematics","type":"journal_article","status":"public","abstract":[{"text":"In a ball $\\Omega \\subset \\mathbb {R}^{n}$ with $n\\ge 2$, the chemotaxis system\r\n\\[ \\left\\{ \\begin{array}{@{}l} u_t = \\nabla \\cdot \\big( D(u)\\nabla u\\big) + \\nabla\\cdot \\big(\\dfrac{u}{v} \\nabla v\\big), \\\\ 0=\\Delta v - uv \\end{array} \\right. \\]is considered along with no-flux boundary conditions for $u$ and with prescribed constant positive Dirichlet boundary data for $v$. It is shown that if $D\\in C^{3}([0,\\infty ))$ is such that $0< D(\\xi ) \\le {K_D} (\\xi +1)^{-\\alpha }$ for all $\\xi >0$ with some ${K_D}>0$ and $\\alpha >0$, then for all initial data from a considerably large set of radial functions on $\\Omega$, the corresponding initial-boundary value problem admits a solution blowing up in finite time.","lang":"eng"}],"volume":153,"date_created":"2024-04-07T12:44:26Z","author":[{"last_name":"Wang","full_name":"Wang, Yulan","first_name":"Yulan"},{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_updated":"2024-04-07T12:44:30Z","publisher":"Cambridge University Press (CUP)","doi":"10.1017/prm.2022.39","title":"Finite-time blow-up in a repulsive chemotaxis-consumption system","issue":"4","publication_identifier":{"issn":["0308-2105","1473-7124"]},"publication_status":"published","page":"1150-1166","intvolume":" 153","citation":{"mla":"Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption System.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 153, no. 4, Cambridge University Press (CUP), 2022, pp. 1150–66, doi:10.1017/prm.2022.39.","short":"Y. Wang, M. Winkler, Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153 (2022) 1150–1166.","bibtex":"@article{Wang_Winkler_2022, title={Finite-time blow-up in a repulsive chemotaxis-consumption system}, volume={153}, DOI={10.1017/prm.2022.39}, number={4}, journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, publisher={Cambridge University Press (CUP)}, author={Wang, Yulan and Winkler, Michael}, year={2022}, pages={1150–1166} }","apa":"Wang, Y., & Winkler, M. (2022). Finite-time blow-up in a repulsive chemotaxis-consumption system. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 153(4), 1150–1166. https://doi.org/10.1017/prm.2022.39","ama":"Wang Y, Winkler M. Finite-time blow-up in a repulsive chemotaxis-consumption system. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2022;153(4):1150-1166. doi:10.1017/prm.2022.39","chicago":"Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption System.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153, no. 4 (2022): 1150–66. https://doi.org/10.1017/prm.2022.39.","ieee":"Y. Wang and M. Winkler, “Finite-time blow-up in a repulsive chemotaxis-consumption system,” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 153, no. 4, pp. 1150–1166, 2022, doi: 10.1017/prm.2022.39."},"year":"2022"},{"language":[{"iso":"eng"}],"_id":"63274","user_id":"31496","abstract":[{"text":"In a ball $\\Omega \\subset \\mathbb {R}^{n}$ with $n\\ge 2$, the chemotaxis system\r\n\\[ \\left\\{ \\begin{array}{@{}l} u_t = \\nabla \\cdot \\big( D(u)\\nabla u\\big) + \\nabla\\cdot \\big(\\dfrac{u}{v} \\nabla v\\big), \\\\ 0=\\Delta v - uv \\end{array} \\right. \\]is considered along with no-flux boundary conditions for $u$ and with prescribed constant positive Dirichlet boundary data for $v$. It is shown that if $D\\in C^{3}([0,\\infty ))$ is such that $0< D(\\xi ) \\le {K_D} (\\xi +1)^{-\\alpha }$ for all $\\xi >0$ with some ${K_D}>0$ and $\\alpha >0$, then for all initial data from a considerably large set of radial functions on $\\Omega$, the corresponding initial-boundary value problem admits a solution blowing up in finite time.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Proceedings of the Royal Society of Edinburgh: Section A Mathematics","title":"Finite-time blow-up in a repulsive chemotaxis-consumption system","doi":"10.1017/prm.2022.39","date_updated":"2025-12-18T20:11:15Z","publisher":"Cambridge University Press (CUP)","author":[{"last_name":"Wang","full_name":"Wang, Yulan","first_name":"Yulan"},{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2025-12-18T19:14:20Z","volume":153,"year":"2022","citation":{"ieee":"Y. Wang and M. Winkler, “Finite-time blow-up in a repulsive chemotaxis-consumption system,” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 153, no. 4, pp. 1150–1166, 2022, doi: 10.1017/prm.2022.39.","chicago":"Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption System.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153, no. 4 (2022): 1150–66. https://doi.org/10.1017/prm.2022.39.","ama":"Wang Y, Winkler M. Finite-time blow-up in a repulsive chemotaxis-consumption system. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2022;153(4):1150-1166. doi:10.1017/prm.2022.39","bibtex":"@article{Wang_Winkler_2022, title={Finite-time blow-up in a repulsive chemotaxis-consumption system}, volume={153}, DOI={10.1017/prm.2022.39}, number={4}, journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, publisher={Cambridge University Press (CUP)}, author={Wang, Yulan and Winkler, Michael}, year={2022}, pages={1150–1166} }","mla":"Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption System.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 153, no. 4, Cambridge University Press (CUP), 2022, pp. 1150–66, doi:10.1017/prm.2022.39.","short":"Y. Wang, M. Winkler, Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153 (2022) 1150–1166.","apa":"Wang, Y., & Winkler, M. (2022). Finite-time blow-up in a repulsive chemotaxis-consumption system. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 153(4), 1150–1166. https://doi.org/10.1017/prm.2022.39"},"page":"1150-1166","intvolume":" 153","publication_status":"published","publication_identifier":{"issn":["0308-2105","1473-7124"]},"issue":"4"},{"type":"journal_article","publication":"Proceedings of the Royal Society of Edinburgh: Section A Mathematics","status":"public","abstract":[{"text":"The paper studies large time behaviour of solutions to the Keller–Segel system with quadratic degradation in a liquid environment, as given byunder Neumann boundary conditions in a bounded domain Ω ⊂ ℝn, where n ≥ 1 is arbitrary. It is shown that whenever U : Ω × (0,∞) → ℝn is a bounded and sufficiently regular solenoidal vector field any non-trivial global bounded solution of (⋆) approaches the trivial equilibrium at a rate that, with respect to the norm in either of the spaces L1(Ω) and L∞(Ω), can be controlled from above and below by appropriate multiples of 1/(t + 1). This underlines that, even up to this quantitative level of accuracy, the large time behaviour in (⋆) is essentially independent not only of the particular fluid flow, but also of any effect originating from chemotactic cross-diffusion. The latter is in contrast to the corresponding Cauchy problem, for which known results show that in the n = 2 case the presence of chemotaxis can significantly enhance biomixing by reducing the respective spatial L1 norms of solutions.","lang":"eng"}],"user_id":"31496","_id":"63369","language":[{"iso":"eng"}],"issue":"5","publication_status":"published","publication_identifier":{"issn":["0308-2105","1473-7124"]},"citation":{"apa":"Cao, X., & Winkler, M. (2018). Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 148(5), 939–955. https://doi.org/10.1017/s0308210518000057","short":"X. Cao, M. Winkler, Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148 (2018) 939–955.","mla":"Cao, Xinru, and Michael Winkler. “Sharp Decay Estimates in a Bioconvection Model with Quadratic Degradation in Bounded Domains.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 148, no. 5, Cambridge University Press (CUP), 2018, pp. 939–55, doi:10.1017/s0308210518000057.","bibtex":"@article{Cao_Winkler_2018, title={Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains}, volume={148}, DOI={10.1017/s0308210518000057}, number={5}, journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, publisher={Cambridge University Press (CUP)}, author={Cao, Xinru and Winkler, Michael}, year={2018}, pages={939–955} }","ieee":"X. Cao and M. Winkler, “Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains,” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 148, no. 5, pp. 939–955, 2018, doi: 10.1017/s0308210518000057.","chicago":"Cao, Xinru, and Michael Winkler. “Sharp Decay Estimates in a Bioconvection Model with Quadratic Degradation in Bounded Domains.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 5 (2018): 939–55. https://doi.org/10.1017/s0308210518000057.","ama":"Cao X, Winkler M. Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2018;148(5):939-955. doi:10.1017/s0308210518000057"},"intvolume":" 148","page":"939-955","year":"2018","author":[{"first_name":"Xinru","full_name":"Cao, Xinru","last_name":"Cao"},{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"date_created":"2025-12-19T11:02:55Z","volume":148,"date_updated":"2025-12-19T11:03:03Z","publisher":"Cambridge University Press (CUP)","doi":"10.1017/s0308210518000057","title":"Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains"}]