Chemotaxis can prevent thresholds on population density

We define and (for $q>n$) prove uniqueness and an extensibility property of $W^{1,q}$-solutions to $u_t =-\nabla\cdot(u\nabla v)+\kappa u-\mu u^2$ $ 0 =\Delta v-v+u$ $\partial_\nu v|_{\partial\Omega} = \partial_\nu u|_{\partial\Omega}=0,$ $ u(0,\cdot)=u_0 $ in balls in $\mathbb{R}^n$, which we then use to obtain a criterion guaranteeing some kind of structure formation in a corresponding chemotaxis system - thereby extending recent results of Winkler to the higher dimensional (radially symmetric) case. Keywords: chemotaxis, logistic source, blow-up, hyperbolic-elliptic system

• Publication year

  2014

• Venue

  arXiv: Analysis of PDEs

• Publication date

  2014-03-07

• Fields of study

  Biology, Mathematics

• Identifiers
  DOI 10.3934/DCDSB.2015.20.1499arXiv 1403.1837
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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