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Systems of \(p\)-Laplacian differential inclusions with large diffusion. (English) Zbl 1191.35163

Summary: We consider coupled systems of \(p\)-Laplacian differential inclusions and we prove, under suitable conditions, that a homogenization process occurs when diffusion parameters become arbitrarily large. In fact we obtain that the attractors are continuous at infinity on \(L^2(\Omega)\times L^2(\Omega )\) topology, with respect to the diffusion coefficients, and the limit set is the attractor of an ordinary differential problem.

MSC:

35K92 Quasilinear parabolic equations with \(p\)-Laplacian
35R70 PDEs with multivalued right-hand sides
35K51 Initial-boundary value problems for second-order parabolic systems
35B41 Attractors
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