On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis
Copyright policy )On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis
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.
Biofilm, Chemotaxis, Attractor, Longtime dynamics, strongly coupled parabolic systems, finite-dimensional global attractor, Degenerate parabolic equations, A priori estimates in context of PDEs, biofilm, 510, 35B41, 35B45, 35D30, 35K65, Mathematics - Analysis of PDEs, Cell movement (chemotaxis, etc.), FOS: Mathematics, Attractor ; Biofilm ; Chemotaxis ; Degenerate Diffusion ; Longtime Dynamics, Attractors, Degenerate diffusion, Initial-boundary value problems for second-order parabolic systems, Weak solutions to PDEs, Analysis of PDEs (math.AP)
Biofilm, Chemotaxis, Attractor, Longtime dynamics, strongly coupled parabolic systems, finite-dimensional global attractor, Degenerate parabolic equations, A priori estimates in context of PDEs, biofilm, 510, 35B41, 35B45, 35D30, 35K65, Mathematics - Analysis of PDEs, Cell movement (chemotaxis, etc.), FOS: Mathematics, Attractor ; Biofilm ; Chemotaxis ; Degenerate Diffusion ; Longtime Dynamics, Attractors, Degenerate diffusion, Initial-boundary value problems for second-order parabolic systems, Weak solutions to PDEs, Analysis of PDEs (math.AP)
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