On a weak attractor of a class of PDEs with degenerate diffusion and chemotaxis

Messoud Efendiev*, Anna Zhigun, Takasi Senba

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this article we deal with a class of degenerate parabolic systems that encompasses two different effects: porous medium and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We prove estimates related to the existence of the global attractor under certain 'balance conditions' on the order of the porous medium degeneracy and the growth of the chemotactic function.

Original languageEnglish
Pages (from-to)1133-1153
JournalJournal of the Mathematical Society of Japan
Volume66
Issue number4
DOIs
Publication statusPublished - 2014

Keywords

  • Attractor
  • Biofilms
  • Chemotaxis
  • Dissipative estimate
  • Porous-medium

ASJC Scopus subject areas

  • Mathematics(all)

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