On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure

Abstract

We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem.

Keywords

• backward in time problem
• dipolar thermoelastic body
• uniqueness of solution
• Cesaro means
• partition of energies