Large time behaviour of solutions for a nonlinear thermoelastic system

We consider a nonlinear thermoelastic system in Rn. We prove the well-posedness and give the decay rate of the energy as t→+∞. Our main tools are the semi-group theory and the Fourier splitting method. We extend some results of Kim (SIAM J. Math. Anal. 23 (1992) 889), Liu and Renardy (Appl. Math. Lett. 8 (1995) 1), and improve the work in Lagnese (SIAM Stud. Appl. Math. 10 (1989)) by proving that it is not necessary to add damping term to get the exponential decay of the solution.