Uniqueness results for a boundary value problem in dipolar thermoelasticity to model composite materials

Composites with microstructure display nonlocal effects and can be effectively modeled through dipolar elasticity. A mixed initial boundary problem is addressed for dipolar thermoelasticity. The basic equations and conditions of the problem are set-up and uniqueness results are proven, which are obtained without introducing definiteness restrictions on the elastic coefficients and, also, without the usual condition imposed to the heat conductivity tensor of being positive definite. An additional result is finally obtained, namely, a reciprocal identity of the Betti's type which underlies another uniqueness result obtained again under weak restrictions.