Galerkin stability of pullback attractors for nonautonomous nonlocal equations

Abstract

We study Galerkin approximation of pullback attractors for a nonautonomous nonlocal parabolic equation. We show that the $ n $th Galerkin approximation system has a pullback attractor in the $ n $-dimensional subspace of the Lebesgue space. We then prove that the sequence of Galerkin pullback attractors is uniformly backward bounded and that the sequence of Galerkin solutions converges uniformly on any bounded set. Using these results, we establish upper semi-convergence of the sequence of Galerkin pullback attractors towards the pullback attractors of the original infinite-dimensional system.