Global attractors for $p$-Laplacian differential inclusions in unbounded domains

Jacson Simsen; José Valero

doi:10.3934/dcdsb.2016096

Article Contents

2016, Volume 21, Issue 9: 3239-3267. Doi: 10.3934/dcdsb.2016096

This issue Previous Article Non-symmetric distorted Brownian motion: Strong solutions, strong Feller property and non-explosion results Next Article Nonlinear stochastic partial differential equations of hyperbolic type driven by Lévy-type noises

Global attractors for $p$-Laplacian differential inclusions in unbounded domains

Jacson Simsen^1, and
José Valero^2,

1.
Instituto de Matemática e Computaçã, Universidade Federal de Itajubá, 37500-903 Itajubá MG
2.
Universidad Miguel Hernández, Centro de Investigación Operativa, Avda. Universidad s/n, Elche (Alicante), 03202

Received: September 30, 2015

Revised: February 29, 2016

Published: October 2016

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Abstract

In this work we consider a differential inclusion governed by a p-Laplacian operator with a diffusion coefficient depending on a parameter in which the space variable belongs to an unbounded domain. We prove the existence of a global attractor and show that the family of attractors behaves upper semicontinuously with respect to the diffusion parameter. Both autonomous and nonautonomous cases are studied.

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Mathematics Subject Classification: 35B40, 35B41, 35K55, 37L3.

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