Diffusion in glassy polymers: Sorption of a finite amount of solvent (Q1806147)

A family of one-dimensional moving boundary models describing the diffusion of a finite amount of a penetrant in a glassy polymer is studied. The local solvability of the associated generic quasilinear system is studied. Also, the global existence and the asymptotic behavior are analyzed. Finally, a rigorous proof is provided for the formal perturbation argument proposed by \textit{D. S. Cohen} and \textit{T. Erneus} [SIAM J. Appl. Math. 48, 1451-1474 (1988; Zbl 0704.35141 and Zbl 0704.35142)], which is used to estimate the rate of convergence of the solution towards the equilibrium.