On certain mathematical models in continuum thermomechanics

This paper presents results on solvability of multidimensional systems of equations of thermoviscoelasticity. Both compressible and incompressible continua are considered. The existence and uniqueness of regular, weak, and weak-renormalized solutions are given, both local and global. The presented results are based on the successive approximation method combined with an a priori estimates, a fixed point argument and passage to the limit technique. The theory of anisotropic Sobolev spaces with a mixed norm and abstract differential equations are used.