Diffusion in Glassy Polymers: Sorption of a Finite Amount of Solvent

A family of 1-D moving boundary models describing the diffusion of a finite amount of a penetrant in a glassy polymer is studied. Local existence of a unique classical solution is obtained for a generic quasilinear model. Specific data are then chosen which can be found in the literature (cf. [6]) and global existence of the classical solution and its convergence to an equilibrium solution are proven. Finally a rigorous proof is provided for a formal perturbation argument proposed in [6] and used therein to estimate the rate of convergence of the solution towards the equilibrium.