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In this paper we study the existence, uniqueness and the asymptotic behavior of the solution of a one dimensional linear thermoelastic system. Such a system is composed of a wave equation coupled with the heat equation and, physically, model the interaction of the vibrations of an elastic string with the variation of its temperature. We prove, first, the existence and uniqueness of solution of the system making use of the Theory of Semigroups of Bounded Linear Operators. For the analysis of the asymptotic behavior of the solution, we use a method consisting of a suitably perturbation to the energy of the system and, with that, we prove that the total energy of the system decays exponentially to zero as t → ∞.

SOBRE O DECAIMENTO EXPONENCIAL DA ENERGIA DE UM SISTEMA TERMOELÁSTICO