Description

• Title:
  Finite-time blow-up in a quasilinear chemotaxis system with an external signal consumption
• Creator:
  Zheng, Pan;
  Mu, Chunlai;
  Hu, Xuegang;
  Wang, Liangchen
• Description:
  This paper deals with a quasilinear chemotaxis system with an external signal consumption \begin{equation*}%\label{1a} \begin{cases} u_t=\nabla\cdot(\varphi(u)\nabla u)-\nabla\cdot(u\nabla v), &(x,t)\in \Omega\times (0,\infty), \\ 0=\Delta v+u-g(x), &(x,t)\in \Omega\times (0,\infty), \end{cases} \end{equation*} under homogeneous Neumann boundary conditions in a ball $\Omega\subset \mathbb{R}^{n}$, where $\varphi(u)$ is a nonlinear diffusion function and $g(x)$ is an external signal consumption. Under suitable assumptions on the functions $\varphi$ and $g$, it is proved that there exists initial data such that the solution of the above system blows up in finite time.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.02.05
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 53, No 1 (March 2019); 25 - 41;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.035/16751 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2018.035/16752
• Subject:
  Finite-time blow-up;
  chemotaxis;
  external signal consumption;
  35K40;
  35K55;
  35B35;
  35B40;
  92C17
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.035
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other