Behaviour of solutions for a thermoelastic Cosserat medium with temperature gradients

Abstract Our study falls within the linear theory of thermoelasticity of Cosserat media. Unlike other works that fall into similar contexts and that use the entropy balance low, our approach is based on an entropy production inequality. The entropy flux tensor is introduced and thermoelastic media are considered for which the stress tensors are dependent on the temperature gradients. In this way, a fourth-order differential equation satisfied by temperature is obtained. In this context the mixed initial-boundary value problem is formulated for which an uniqueness result regarding the solution of this problem is proven. Also, a continuous dependence result is deduced for the solution of the mixed formulated problem with regard to the charges and the initial values.