On an exponential attractor for a class of pdes with degenerate diffusion and chemotaxis

Messoud Efendiev, Anna Zhigun

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
153 Downloads (Pure)

Abstract

In this article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We show the existence of an exponential attractor and, hence, of a finite-dimensional global attractor under certain 'balance conditions' on the order of the degeneracy and the growth of the chemotactic function.
Original languageEnglish
Pages (from-to)651-673
Number of pages23
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume38
Issue number2
DOIs
Publication statusPublished - 01 Feb 2018

Keywords

  • Attractor
  • Biofilm
  • Chemotaxis
  • Degenerate diffusion
  • Longtime dynamics

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