Structure and regularity of the global attractor of a reaction-di{\S}usion equation with non-smooth nonlinear term

TL;DR

This paper investigates the structure of the global attractor for a reaction-diffusion equation with non-smooth nonlinearities, highlighting how it can be characterized via unstable and stable manifolds despite non-uniqueness issues.

Contribution

It provides a novel characterization of the global attractor using unstable and stable manifolds in a non-uniqueness setting for reaction-diffusion equations.

Findings

Global attractor characterized by unstable manifold of stationary points

Stable manifold characterization using bounded complete trajectories

Addresses non-uniqueness in reaction-diffusion equations

Abstract

In this paper we study the structure of the global attractor for a reaction- di{\S}usion equation in which uniqueness of the Cauchy problem is not guarantied. We prove that the global attractor can be characterized using either the unstable manifold of the set of stationary points or the stable one but considering in this last case only solutions in the set of bounded complete trajectories.