Dynamics of parabolic equations via the finite element method I. Continuity of the set of equilibria

Abstract

In this paper we study the dynamics of parabolic semilinear differential equations with homogeneous Dirichlet boundary conditions via the discretization of finite element method. We provide an appropriate functional setting to treat this problem and, as a first step, we show the continuity of the set of equilibria and of its linear unstable manifolds.