Robustness of dynamically gradient multivalued dynamical systems

TL;DR

This paper investigates the robustness of dynamically gradient multivalued semiflows and applies the findings to analyze the dynamical properties of Chafee-Infante problems approximating a differential inclusion, demonstrating the generation of a multivalued semiflow.

Contribution

It introduces a new analysis of the robustness of multivalued semiflows and applies it to specific differential inclusion problems, establishing their dynamical properties.

Findings

Weak solutions generate a dynamically gradient multivalued semiflow.

Application to Chafee-Infante problems shows the semiflow structure.

Proves the stability of the semiflow under approximations.

Abstract

In this paper we study the robustness of dynamically gradient multivalued semiflows. As an application, we describe the dynamical properties of a family of Chafee-Infante problems approximating a differential inclusion studied in [3], proving that the weak solutions of these problems generate a dynamically gradient multivalued semiflow with respect to suitable Morse sets.