Coupled nonautonomous inclusion systems with spatially variable exponents

摘要

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