  We prove global existence of a solution to an initial and boundary value
problem for a highly nonlinear PDE system. The problem arises from a
thermomechanical dissipative model describing hydrogen storage by use of metal
hydrides. In order to treat the model from an analytical point of view, we
formulate it as a phase transition phenomenon thanks to the introduction of a
suitable phase variable. Continuum mechanics laws lead to an evolutionary
problem involving three state variables: the temperature, the phase parameter
and the pressure. The problem thus consists of three coupled partial
differential equations combined with initial and boundary conditions. Existence
and regularity of the solutions are here investigated by means of a time
discretization-a priori estimates-passage to the limit procedure joined with
compactness and monotonicity arguments.
