A Dissipative Model for Hydrogen Storage: Existence and Regularity Results

TL;DR

This paper establishes the global existence and regularity of solutions for a complex PDE system modeling hydrogen storage in metal hydrides, using advanced analytical techniques to handle the nonlinear, coupled equations.

Contribution

It provides a rigorous mathematical proof of existence and regularity for a thermomechanical PDE model of hydrogen storage, formulated as a phase transition problem.

Findings

Proved global existence of solutions to the PDE system.

Established regularity properties of the solutions.

Developed analytical methods for nonlinear coupled PDEs in thermomechanics.

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 thermomechanical 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. 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.