On the hyperbolic thermoelasticity with several dissipation mechanisms

In this work, we study a two-dimensional problem involving a thermoelastic body with four dissipative mechanisms. The well-known theory proposed by Lord and Shulman is used. The existence and uniqueness of solution is proved by using theory of linear semigroups. Then, introducing some assumptions of the coupling coefficients, we prove that the energy decay is exponential. An extension to the theory provided by Green and Lindsay is briefly presented and to the three-dimensional case is also commented.