Equações de reação-difusão com expoentes variáveis e problema limite semilinear

Abstract

We will study nonlinear reaction-diffusion problems involving the p(x)-Laplacian operator. Our study addresses the issues of existence of solution and global attractors for the equations focusing primarily on the stability of partial differential equations with respect to initial conditions and variable exponents. We will examine the continuity of the flow and the upper semicontinuity of the attractors in the family of global attractors of the reaction-diffusion equations with variable exponents, when the exponents converge to 2 in the space of essentially bounded functions. In this scenario, the limiting problem is semilinear, with the p(x)-Laplacian operator converging to the Laplacian operator.