SAINT-VENANTS-PRINCIPLE AND UNIQUENESS RESULTS IN LINEAR THERMOELASTICITY WITH MEMORY FOR HEAT-FLUX

The motion of a linear thermoelastic body of an arbitrary regular shap e is studied when the loadings are applied consisting of body and boun dary supplies and initial conditions. It is shown that, provided the l oadings possess a bounded support (D) over cap(T)$, on the time interv al [0, T], an energetic measure depending on t is an element of [0, T] and on the distance r from support (D) over cap(T)$ (i) vanishes for r greater than or equal to chi t, chi = const., chi > 0; or (ii) decay s to zero for r less than or equal to chi t, the decay rate being cont rolled by the factor I -r/chi t. A uniqueness result is established fo r an unbounded body without any kind of a priori restriction on the gr owth of the solution at infinity.