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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 thermo‐mechanical 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. The existence and regularity of the solutions are here investigated by means of a time discretization—textita priori estimates—passage to the limit procedure joined with compactness and monotonicity arguments. Copyright © 2010 John Wiley & Sons, Ltd.

A dissipative model for hydrogen storage: existence and regularity results