WIAS Preprint No. 2312, (2016)

The full Keller--Segel model is well-posed on fairly general domains



Authors

  • Horstmann, Dirk
  • Rehberg, Joachim
  • Meinlschmidt, Hannes

2010 Mathematics Subject Classification

  • 35A01 35K45 35K57 35Q92 92C17

Keywords

  • Partial differential equations, Keller-Segel system, chemotaxis, reaction-crossdiffusion system, nonsmooth domains

Abstract

In this paper we prove the well-posedness of the full Keller-Segel system, a quasilinear strongly coupled reaction-crossdiffusion system, in the spirit that it always admits a unique local-in-time solution in an adequate function space, provided that the initial values are suitably regular. Apparently, there exists no comparable existence result for the full Keller-Segel system up to now. The proof is carried out for general source terms and is based on recent nontrivial elliptic and parabolic regularity results which hold true even on fairly general spatial domains, combined with an abstract solution theorem for nonlocal quasilinear equations by Amann.

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