The area of partial differential equations that concerns the mathematical theory of the equations of thermomechanics has been a testing ground of several analytical ideas in the theory of nonlinear partial differential equations and in turn a domain of development for numerical methods. The advent of modern material science presents various new challenges to this area. The goal of this minicourse is to present some of the analytical ideas and open problems in the area of thermomechanics, with a goal to identify important elements of the structure of the equations.

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