Spectral approximations of attractors of a class of semilinear parabolic equations

Abstract

Suppose a semigroup, generated by a semilinear parrabolic equation, admits a local, compact attractor. We consider a finite-dimensional approximation of the equation by a numerical scheme which includes the three classical spectral methods: Galerkin, Tau and Collocation. We give conditions to ensure that each approximate semigroup has a local, compact attractor and we analyze the convergence of such discrete attractors to the original one.