Uniform stabilisation of a thermoelastic system with static Wentzell conditions

Abstract

In this paper, we consider a thermoelastic system with static Wentzell boundary conditions. We show the well-posedness, using the semigroup theory, and establish an explicit decay rate result, using the multiplier method. More precisely, we prove an exponential decay result under the influence of competing both boundary damping and localised interior damping . Our method consists in establishing a crucial fundamental identity and exploiting it to derive the decay rates.