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Zbl 1191.35163
Simsen, Jacson; Gentile, Cláudia B.
Systems of $p$-Laplacian differential inclusions with large diffusion. (English)
[J] J. Math. Anal. Appl. 368, No. 2, 525-537 (2010). ISSN 0022-247X

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 2000:: *35K92
35R70 PDE with multivalued right-hand sides
35K51
35B41 Attractors

Keywords: reaction-diffusion systems; homogenization process; limit set

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Zentralblatt MATH Berlin [Germany]