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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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter 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 Band: 38, Heft: 2, Seiten: 651-673 Artikelnummer: , Supplement: ,
Verlag American Institute of Mathematical Sciences (AIMS)
Verlagsort Springfield
Begutachtungsstatus Peer reviewed