Well-Posedness and Stability for Semilinear Thermoelastic System with Boundary Time-Varying Delay and Nonlinear Weight (Journal of Partial Differential Equations, 2025)
This paper is concerned with the well-posedness, uniform asymptotic stability and dynamics for a semilinear thermoelastic system with time-varying delayboundary feedback and nonlinear weight, which can be used to describe the physicalprocedure of meridian retraction and release therapy. The perturbation theory of linearoperators by Kato is used to deal with the invalidity of Lumper-Phillips theorem onnon-autonomous PDEs operator, the multiplier approach and quasi-stability methodlead to the stability and dynamics for our semilinear problem, which are also true forlinear thermoelastic system without weight.
Keywords: Semilinear thermoelastic system; quasi-stability; time-varying delay; Kato’s perturbation method.