Edwards, David A.; Cairncross, Richard A. Desorption overshoot in polymer-penetrant systems: Asymptotic and computational results. (English) Zbl 1011.35011 SIAM J. Appl. Math. 63, No. 1, 98-115 (2002). Summary: Many practically relevant polymers undergoing desorption change from the rubbery (saturated) to the glassy (nearly dry) state. The dynamics of such systems cannot be described by the simple Fickian diffusion equation due to viscoelastic effects. The mathematical model solved numerically is a set of two coupled PDEs for concentration and stress. Asymptotic solutions are presented for a moving boundary-value problem for the two states in the short-time limit. The solutions exhibit desorption overshoot, where the penetrant concentration in the interior is less than that on the surface. In addition, it is shown that if the underlying time scale of the equations is ignored when postulating boundary conditions, nonphysical solutions can result. Cited in 7 Documents MSC: 35B20 Perturbations in context of PDEs 35C20 Asymptotic expansions of solutions to PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35R35 Free boundary problems for PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 74D10 Nonlinear constitutive equations for materials with memory 76M10 Finite element methods applied to problems in fluid mechanics 35C15 Integral representations of solutions to PDEs 80A22 Stefan problems, phase changes, etc. Keywords:asymptotic expansions; viscoelastic effects; moving boundary-value problems; perturbation methods; polymer-penetrant systems; finite-element method Software:DASSL PDFBibTeX XMLCite \textit{D. A. Edwards} and \textit{R. A. Cairncross}, SIAM J. Appl. Math. 63, No. 1, 98--115 (2002; Zbl 1011.35011) Full Text: DOI