OLDER TYPE STABILITY OF CONTINUATION FOR THE LINEAR THERMOELASTICITY SYSTEM WITH RESIDUAL STRESS

By introducing some auxiliary functions, an elasticity system with thermal eects becomes a coupled hyperbolic-parabolic system. Using this reduced system, we obtain a Carleman estimate with two large parameters for the linear thermoelasticity system with residual stress which is the basic tool for showing stability estimates in the lateral Cauchy problem. eld. Most solids exhibit a volumetric change with temperature variation, and thus the presence of a temperature distribution generally induces stresses created from boundary or internal constraints. The thermal component is natural for residual stress modeling used in many engineering and geophysical applications. This residual stress might be induced by thermal changes due to cooling or heating, so the temperature changes cannot be ignored. Thermal stresses exist whenever temperature gradients are present in a material body. In general, residual stress is anisotropic (15). Therefore its possible source cannot be assumed to be isotropic. Hence we consider a general parabolic second order partial dierential operator to model this thermal eect. In this paper we obtain Carleman estimates with a second large parameter and a general weight function for a second order parabolic partial dierential operator and the linear thermoelasticity system with residual stress. Based on this Carleman estimate, we prove Holder stability for the Cauchy problem of thermoelasticity system with residual stress. Here we let x2 R 3 and (x;t)2 = G ( T;T ) R 4 . The residual stress is modeled by a symmetric second-rank tensor R(x) = (rjk(x)) 3=1 2 C 2 ( ) which is divergence free,r R = 0. Let u(x;t) = (u1;u2;u3) > : ! R 3 be the displacement vector in . The temperature is given by = (x;t).