S. Jiang et al., ASYMPTOTIC STABILITY AND GLOBAL EXISTENCE IN THERMOELASTICITY WITH SYMMETRY, Quarterly of applied mathematics, 56(2), 1998, pp. 259-275
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.