The stability and rapid exponential stabilization of heat equation in non-cylindrical domain

TL;DR

This paper investigates the stability of the heat equation in non-cylindrical domains, identifying conditions for polynomial or weak stability, and introduces a backstepping method for rapid exponential stabilization.

Contribution

It provides new insights into stability conditions for heat equations in non-cylindrical domains and develops a backstepping approach for rapid stabilization.

Findings

Certain initial values lead to non-exponential stability.

The system can be stabilized exponentially using backstepping.

The paper extends stabilization techniques to non-cylindrical domains.

Abstract

This paper is devoted to the study of the stability and stabilizability of heat equation in non-cylindrical domain. The interesting thing is that there is a class of initial values such that the system is no longer exponentially stable. The system is only polynomially stable or only analogously exponentially stable. Then, the rapid exponential stabilization of the system is obtained by the backstepping method.