Abstract. In this paper, we shall establish some global existence results for a 3D hyperbolic system arising from Green-Naghdi models of thermoelasticity of type II with a dissipative boundary condition for the displacement. The existence and exponential decay of energy for the linear problem has been solved by Lazzari and Nibbi, Journal of Mathematical Analysis and Applications, 338 (2008), 317-329. Furthermore, we shall establish the global existence of solutions to semilinear and nonlinear thermoelastic systems by using the semigroup approach.

a b s t r a c tIn this paper, we prove the global existence and exponential stability of solutions to nonlinear thermoelastic equations with second sound provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.