Growth and uniqueness in thermoelasticity

A uniqueness theorem is proved for two theories of thermoelasticity capable of admitting finite speed thermal waves, the theories having been proposed by Green & Naghdi. Uniqueness is proved under the weak assumption of requi ring only major symmetry of the elasticity tensor; no definiteness whatsoev er is postulated. It is shows how to demonstrate uniqueness by a Lagrange i dentity method and also by producing a novel functional to which to apply t he technique of logarithmic convexity. It is remarked on how to extend the result to an unbounded spatial domain without requiring decay restrictions on the solution at infinity. Finally, conditions are derived which show hop i a suitable measure of the solution will grow at least exponentially in ti me if the initial 'energy' satisfies appropriate conditions. This complemen ts the fundamental work of Knops & Payne, who produced corresponding growth results in the isothermal elasticity case.