A dissipative model for hydrogen storage: existence and regularity results

Abstract

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-a priori estimates-passage to the limit procedure joined with compactness and monotonicity arguments.

Global existence for a hydrogen storage model with full energy balance

“…In order to prove Theorem 2.2, we introduce a regularizing term in (2.20), take advantage of the results shown by Chiodaroli in [8], prove uniform estimates and then pass to the limit with respect to the approximation parameter.…”

“…The auxiliary variable e is prescribed in terms of θ and χ by relation (1.2) via the smooth function ψ. In fact, ψ satisfies all the good properties we need (in particular, invertibility with respect to the first variable) since the function h is smooth and small enough (see [4,8]): more precisely, we assume that there exists a constant c h > 1 such that…”

“…Following a usual approach in thermodynamics, Bonetti, Frémond and Lexcellent [4] derived the governing equilibrium equations (actually simplifying some physical assumptions, but ensuring thermodynamical consistency). The model has next been resumed and extended in [8].…”

“…For this reason, the authors of [4] suppressed it in the first analysis they carried out after the derivation of the model. That term is instead maintained in [8], where equation (1.3) is replaced by…”

Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system

“…With reference to such a complete discretization of Cahn-Hilliard and viscous Cahn-Hilliard systems, we quote papers [1,2,3,4,5,6,7,8,22,21,23]. Some recent efforts can be found in the literature with the aim of analyzing other classes of phase transition problems, either to show existence via time discretization [9,14,15,19,20,27,30,35,36] or to prove numerical results such as special convergence properties, stability or error estimates [11,12,13,18,25,28,31,33,34] (cf. also [26] for a recent review on phase-field models).…”