Coupled nonautonomous inclusion systems with spatially variable exponents

Abstract

A family of nonautonomous coupled inclusions governed by $p(x)$-Laplacian operators with large diffusion is investigated. The existence of solutions and pullback attractors as well as the generation of a generalized process are established. It is shown that the asymptotic dynamics is determined by a two dimensional ordinary nonautonomous coupled inclusion when the exponents converge to constants provided the absorption coefficients are independent of the spatial variable. The pullback attractor and forward attracting set of this limiting system is investigated.

Keywords

• nonautonomous parabolic problems
• variable exponents
• pullback attractors
• omega limit sets
• upper semicontinuity