On a Global Uniform Pullback Attractor of a Class of PDEs with Degenerate Diffusion and Chemotaxis in One Dimension

Messoud Efendiev*, Anna Zhigun

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

In this chapter, we deal with a class of nonautonomous 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. Under certain "balance" conditions on the order of the porous medium degeneracy and the growth of the chemotactic function, we establish the existence of a strong uniform pull back attractor for the case of one spatial dimension, thus improving our previous study, where a weak attractor was constructed.

Original languageEnglish
Title of host publicationRecent Trends in Dynamical Systems - Proceedings of a Conference in Honor of Jurgen Scheurle
PublisherSpringer New York LLC
Pages179-203
Number of pages25
Volume35
ISBN (Print)9783034804509
DOIs
Publication statusPublished - 01 Jan 2013
Externally publishedYes
Event2012 International Conference Recent Trends in Dynamical Systems - Munich, Germany
Duration: 11 Jan 201213 Jan 2012

Conference

Conference2012 International Conference Recent Trends in Dynamical Systems
CountryGermany
CityMunich
Period11/01/201213/01/2012

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'On a Global Uniform Pullback Attractor of a Class of PDEs with Degenerate Diffusion and Chemotaxis in One Dimension'. Together they form a unique fingerprint.

Cite this