A type III thermoelastic problem with mixtures

Abstract

In this work we study a thermoelastic problem involving binary mixtures. Type III thermal theory is considered for the modeling of the heat conduction. Existence, uniqueness and continuous dependence of solutions are proved by using the semigroup theory. Then, the numerical analysis of the resulting variational problem is considered, by using the finite element method for the spatial approximation and the implicit Euler scheme to discretize the time derivatives. An a priori error analysis is performed and the linear convergence is derived under adequate additional regularity conditions. Finally, some numerical examples involving one- and two-dimensional examples are shown to demonstrate the convergence of the approximations and the behavior of the solution