  A thermo-mechanical model describing hydrogen storage by use of metal
hydrides has been recently proposed in a paper by Bonetti, Fr\'emond and
Lexcellent. It describes the formation of hydrides using the phase transition
approach. By virtue of the laws of continuum thermo-mechanics, the model leads
to a phase transition problem in terms of three state variables: the
temperature, the phase parameter representing the fraction of one solid phase,
and the pressure, and is derived within a generalization of the principle of
virtual powers proposed by Fr\'emond accounting for micro-forces, responsible
for the phase transition, in the whole energy balance of the system. Three
coupled nonlinear partial differential equations combined with initial and
boundary conditions have to be solved. The main difficulty in investigating the
resulting system of partial differential equations relies on the presence of
the squared time derivative of the order parameter in the energy balance
equation. Here, the global existence of a solution to the full problem is
proved by exploiting known and sharp estimates on parabolic equations with
right hand side in L^1. Some complementary results on stability and steady
state solutions are also given.
