Implications of the Lagrange Identity in Thermoelasticity of Dipolar Bodies

Abstract

This paper is concerned with the mixed initial-boundary value problem in the context of the theory of thermoelasticity of dipolar bodies. We prove a uniqueness theorem and some continuous dependence theorems without recourse to any energy conservation law, or to any boundedness assumptions on the thermoelastic coefficients. This was possible due to the use of Lagrange’s identity. Because of the flexibility of this identity, we also avoid the use of positive definiteness assumptions on the thermoelastic coefficients.