Some results on stability and continuous dependence in Green-Naghdi thermoelasticity of Cosserat bodies

Abstract

In our paper, we consider the mixed problem in the context of the Green-Naghdi theory of thermoelastic Cosserat media. Using very accessible mathematical calculations, we prove two qualitative results on the solutions of the formulated mixed problem. Thus, in the first of these approaches, we obtain a result of stability, of the Hölder type, with regards to the loads. In the second main result, we prove a continuous dependence result regarding the initial values from the mixed problem. It should be noted that we obtain these results without imposing very restrictive conditions on the thermoelastic tensors in the constitutive equations. In fact, imposed restrictions are commonly used in Mechanics of Continuous Media.