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

Messoud Efendiev; Anna Zhigun

doi:10.3934/dcds.2018028

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2018, Volume 38, Issue 2: 651-673. Doi: 10.3934/dcds.2018028

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

Messoud Efendiev^1, and
Anna Zhigun^2, ,

1.
Institute of Computational Biology, Helmholtz Zentrum München, Ingolstädter Landstr. 1,85764 Neuherberg, Germany
2.
Felix-Klein-Zentrum für Mathematik, Technische Universität Kaiserslautern, Paul-Ehrlich-Str. 31,67663 Kaiserslautern, Germany

* Corresponding author: Anna Zhigun
* Corresponding author: Anna Zhigun

Received: April 30, 2017

Revised: August 31, 2017

Published: November 2017

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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.

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Mathematics Subject Classification: Primary: 35B41, 35K65; Secondary: 35B45, 35D30.

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