Long-time behavior for a nonlinear parabolic problem with variable exponents

Abstract

This paper addresses the question of the asymptotic behavior of solutions to the p(x)-Laplacian problem ut−div(|∇u|p(x)−2∇u)+f(x,u)=g. With general assumptions on f(x,u) and the exponent p(x), we prove the existence of global attractors in proper spaces. Then we consider the fractal dimension of global attractors for the problem. Under suitable conditions, we show that the problem admits an infinite-dimensional global attractor.