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 requiring only major symmetry of the elasticity tensor; no definiteness whatsoever is postulated. It is shows how to demonstrate uniqueness by a Lagrange identity method and also by producing a novel functional to which to apply the 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 hopi a suitable measure of the solution will grow at least exponentially in time if the initial 'energy' satisfies appropriate conditions. This complements the fundamental work of Knops & Payne, who produced corresponding growth results in the isothermal elasticity case.