Quantitative and stability study of the evolution of a thermoelastic body

Abstract

We prove the existence and uniqueness of a solution to a system of equations describing the evolution of a linear thermoelastic body by using a semi-group method. Moreover, the uniform exponential stability of the solution is shown in a particular case.•With respect to the existence and uniqueness of the solution, we have defined a linear operator which generates a contraction semi-group and show that it is monotone maximal.•With respect to the stability of the system, we have computed explicitly the expression of the solution of the system and show that the semi-group is uniformly exponentially stable in a particular case.