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Efendiyev, M.A. ; Zhigun, A.*

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

Discrete Contin. Dyn. Syst.-Ser. A 38, 651-673 (2018)
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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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Publication type Article: Journal article
Document type Scientific Article
Keywords Attractor ; Biofilm ; Chemotaxis ; Degenerate Diffusion ; Longtime Dynamics; Infinite-dimensional Attractors; Porous-medium Equation; Growth System; Parabolic Equations; Weak Solutions; P-laplacian; Continuity; Regularity; Boundary
ISSN (print) / ISBN 1078-0947
e-ISSN 1553-5231
Quellenangaben Volume: 38, Issue: 2, Pages: 651-673 Article Number: , Supplement: ,
Publisher American Institute of Mathematical Sciences (AIMS)
Publishing Place Springfield
Reviewing status