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On a weak attractor of a class of PDEs with degenerate diffusion and chemotaxis. (English) Zbl 1348.35036

Authors’ abstract: In this article we deal with a class of degenerate parabolic systems that encompasses two different effects: porous medium and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We prove estimates related to the existence of the global attractor under certain “balance conditions” on the order of the porous medium degeneracy and the growth of the chemotactic function.

MSC:

35B41 Attractors
35B45 A priori estimates in context of PDEs
35K65 Degenerate parabolic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35D30 Weak solutions to PDEs
92C17 Cell movement (chemotaxis, etc.)
35K40 Second-order parabolic systems
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