Asymptotic convergence of solutions for Laplace reaction-diffusion equations

We study the initial-boundary value problem for a Laplace reaction-diffusion equation. After constructing local solutions by using the theory of abstract degenerate evolution equations of parabolic type, we show asymptotic convergence of bounded global solutions if they exist under the assumption that the reaction function is analytic in neighborhoods of their w-limit sets. Reduction of degenerate evolution equation to multivalued evolution equation enables us to use the theory of the infinite-dimensional Lojasiewicz-Simon gradient inequality. (C) 2019 The Authors. Published by Elsevier Ltd.