Global existence for a hydrogen storage model with full energy balance

A thermo-mechanical model describing hydrogen storage by use of metal hydrides has been recently proposed in Bonetti et al. (2007) describing the formation of hydrides using the phase transition approach. The model is derived within the framework of phase transitions and it is written in terms of three state variables: the temperature, the phase parameter (representing the fraction of one solid phase), and the pressure. The equations come from the laws of thermo-mechanics, by use of a generalized principle of virtual powers that has been proposed by Frmond (2002). In particular, the whole energy balance of the system accounts for micro-forces, which are responsible for the phase transition. 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, and actually this term was neglected in the analysis performed in Bonetti et al. (2007). Here, the global existence of a solution to the full problem is proved by exploiting known and sharp estimates on parabolic equations with the right hand side in L1. Some complementary results on stability and steady state solutions are also given.