SINGULAR PERTURBATIONS AND THE COUPLED QUASI-STATIC APPROXIMATION IN LINEAR THERMOELASTICITY

A uniform asymptotic expansion in the inertial constant epsilon is given for one-dimensional linear thermoelasticity by a two-timing method. The result shows that the usual coupled/quasi-static approximation (epsilon = 0) is not uniformly asymptotically correct even to lowest order. The interaction between diffusion and wave propagation is clearly displayed. The proof of uniform asymptotic validity to order epsilon2 is accomplished by energy estimates.