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.

Keywords

• Semi group method