Well-Posedness and Stability for Semilinear Thermoelastic System with Boundary Time-Varying Delay and Nonlinear Weight

Abstract

This paper is concerned with the well-posedness, uniform asymptotic sta- bility and dynamics for a semilinear thermoelastic system with time-varying delay boundary feedback and nonlinear weight, which can be used to describe the physical procedure of meridian retraction and release therapy. The perturbation theory of linear operators by Kato is used to deal with the invalidity of Lumper-Phillips theorem on non-autonomous PDEs operator, the multiplier approach and quasi-stability method lead to the stability and dynamics for our semilinear problem, which are also true for linear thermoelastic system without weight.

Keywords

Semilinear thermoelastic system / quasi-stability / time-varying delay / Kato’s pertur- bation method