Stability properties of dissipative evolution equations with nonautonomous and nonlinear damping

TL;DR

This paper investigates the stability of dissipative evolution equations with nonautonomous and nonlinear damping, providing new theoretical results and concrete examples demonstrating stability properties.

Contribution

It introduces novel stability results for nonlinear, nonautonomous dissipative equations using comparison principles and exponential stability of linear autonomous cases.

Findings

Established well-posedness for certain nonlinear nonautonomous equations.

Proved stability results for specific dissipative evolution equations.

Illustrated theoretical results with concrete examples.

Abstract

In this paper, we obtain some stability results of (abstract) dissipative evolution equations with a nonautonomous and nonlinear damping using the exponential stability of the retrograde problem with a linear and autonomous feedback and a comparison principle. We then illustrate our abstract statements for different concrete examples, where new results are achieved. In a preliminary step, we prove some well-posedness results for some nonlinear and nonautonomous evolution equations.