  A thermodynamically consistent mathematical model for hydrogen adsorption in
metal hydrides is proposed. Beside hydrogen diffusion, the model accounts for
phase transformation accompanied by hysteresis, swelling, temperature and heat
transfer, strain, and stress. We prove existence of solutions of the ensuing
system of partial differential equations by a carefully-designed, semi-implicit
approximation scheme. A generalization for a drift-diffusion of multi-component
ionized "gas" is outlined, too.
