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

Messoud Efendiev | Zendy; Anna Zhigun | Zendy

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

Author(s) -

Messoud Efendiev,

Anna Zhigun

Publication year - 2017

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2018028

Subject(s) - attractor , chemotaxis , degenerate energy levels , degeneracy (biology) , exponential function , class (philosophy) , diffusion , exponential growth , function (biology) , mathematics , physics , mathematical analysis , computer science , quantum mechanics , biology , bioinformatics , biochemistry , receptor , artificial intelligence , evolutionary biology

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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