Considerations About Classical and Weak Solutions in a Thermoelastic Cosserat Body with Voids

In our study we consider the mixed problem with initial data and boundary values in the theory of the thermoelastic Cosserat media having pores. We included a new constitutive independent variable, namely the derivative of the function of pores with respect to the time variable. After that we address the problem of the uniqueness of the solution of the formulated mixed problem and demonstrate the uniqueness of the solution under not very restrictive conditions. Regarding the uniqueness, we made some considerations on the waves of dilatational kind for this type of body. Another important result of our study is relative to weak solutions for the mixed problem. After formulating this type of solution and systematizing the initial and boundary conditions for the existence of such a type of solution, some abstract results from the theory of differential equations were adapted to prove both, i.e., the existence and the uniqueness of the mentioned solution.