ASYMPTOTIC STABILITY AND GLOBAL EXISTENCE IN THERMOELASTICITY WITH SYMMETRY

First we prove an exponential decay result for solutions of the equati ons of linear, homogeneous, isotropic thermoelasticity in bounded regi ons in two or three space dimensions if the rotation of the displaceme nt vanishes. As a consequence, we describe the decay in radially symme trical situations, and in a cylinder in R-3. Then we establish the glo bal existence of solutions to the corresponding nonlinear equations fo r small smooth initial data and a certain class of nonlinearities.