Asymptotic stability and global existence in thermoelasticity with symmetry

First we prove an exponential decay result for solutions of the equations of linear, homogeneous, isotropic thermoelasticity in bounded regions in two or three space dimensions if the rotation of the displacement vanishes. As a consequence, we describe the decay in radially symmetrical situations, and in a cylinder in R-3. Then we establish the global existence of solutions to the corresponding nonlinear equations for small smooth initial data and a certain class of nonlinearities.