Lipschitz perturbations of the Chafee-Infante equation

In this paper we deal with Lipschitz perturbations (not differentiable) of the well-known Chafee-Infante equation. We show the permanence and stability for each equilibrium points and we prove a Lipschitz version of the Hartman-Grobman theorem to construct a local homeomorphism that conjugates orbits in a neighborhood of each equilibrium points. We also prove the continuity of attractors under Lipschitz perturbations. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this paper, the authors study Lipschitz perturbations of the Chafee-Infante equation, which is not differentiable. They prove the permanence and stability of equilibrium points and establish a Lipschitz version of the Hartman-Grobman theorem to find a local homeomorphism that maps orbits near each equilibrium point. The authors also demonstrate the continuity of attractors under Lipschitz perturbations.