Persistence in nonautonomous quasimonotone parabolic partial functional differential equations with delay

TL;DR

This paper develops a dynamical framework for non-autonomous delayed parabolic PDEs, establishing conditions for persistence and continuous separation over minimal sets, advancing understanding of long-term behavior in such systems.

Contribution

It introduces criteria for persistence and continuous separation in non-autonomous delayed parabolic PDEs, extending dynamical systems theory to these equations.

Findings

Conditions for continuous separation of type II over minimal sets

Criteria for uniform and strict persistence

Framework applicable to non-autonomous delayed PDEs

Abstract

This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II over a minimal set are given. Then, practical criteria for the uniform or strict persistence of the systems above a minimal set are obtained.