Finite-time blow-up in a repulsive chemotaxis-consumption system

article Finite-time blow-up in a repulsive chemotaxis-consumption system published Yulan Wang author Michael Winkler author In a ball $\Omega \subset \mathbb {R}^{n}$ with $n\ge 2$, the chemotaxis system \[ \left\{ \begin{array}{@{}l} u_t = \nabla \cdot \big( D(u)\nabla u\big) + \nabla\cdot \big(\dfrac{u}{v} \nabla v\big), \\ 0=\Delta v - uv \end{array} \right. \]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. Cambridge University Press (CUP)2022 eng General Mathematics Proceedings of the Royal Society of Edinburgh: Section A Mathematics 0308-2105 1473-712410.1017/prm.2022.39 15341150-1166 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:<a href="https://doi.org/10.1017/prm.2022.39">10.1017/prm.2022.39</a> @article{Wang_Winkler_2022, title={Finite-time blow-up in a repulsive chemotaxis-consumption system}, volume={153}, DOI={<a href="https://doi.org/10.1017/prm.2022.39">10.1017/prm.2022.39</a>}, 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} } 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:<a href="https://doi.org/10.1017/prm.2022.39">10.1017/prm.2022.39</a>. 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. <a href="https://doi.org/10.1017/prm.2022.39">https://doi.org/10.1017/prm.2022.39</a>. Y. Wang, M. Winkler, Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153 (2022) 1150–1166. 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. <a href="https://doi.org/10.1017/prm.2022.39">https://doi.org/10.1017/prm.2022.39</a> 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: <a href="https://doi.org/10.1017/prm.2022.39">10.1017/prm.2022.39</a>. 533312024-04-07T12:44:26Z2024-04-07T12:44:30Z