  This paper deals with the study of a three-dimensional model of
thermomechanical coupling for viscous solids exhibiting hysteresis effects.
This model is written in accordance with the formalism of generalized standard
materials and it is composed of the momentum equilibrium equation combined with
the flow rule, which describes some stress-strain dependance, coupled to the
heat-transfer equation. More precisely, the coupling terms are linear with
respect to the temperature and the displacement and non linear with respect to
the internal variable. The main mathematical difficulty lies in the fact that
the natural framework for the right-hand side of the heat equation is the space
of L1 functions. A local existence result for this thermodynamically consistent
problem is obtained by using a fixed-point argument. Then the solutions are
proved to be physically admissible and global existence is discussed under some
additional assumptions on the data.

Analysis of PDEs;Functional Analysis