Global existence of solutions to a hydrogen storage model

In this paper we review some existence results obtained for a thermo-mechanical model describing hydrogen storage by use of metal hydrides, based on the phase transition approach. The model is written in terms of three state variables: the absolute temperature, a phase parameter (standing for the fraction of one solid phase), and the pressure. The equations result from the general laws of thermo-mechanics, by introducing a generalized form of the principle of virtual power, as proposed by Michel Fremond. The PDE system combines three coupled nonlinear partial differential equations with related initial and boundary conditions. The main difficulty in the analysis relies on the presence of the squared time derivative of the order parameter in the energy balance equation. In a recent joint collaboration we could surmount this difficulty by exploiting sharp estimates on parabolic equations with right hand side in L^1. Morever, and this is the new contribution from this note, we can prove that under suitable assumptions on the data and in the 1D case our weak solution is actually strong.