'The Japan Society for Industrial and Applied Mathematics'
Doi
Abstract
In the context of analyzing a new model for nonlinear diffusion in polymers, an
unusual condition appears at the moving interface between the glassy and rubbery phases of the
polymer. This condition, which arises from the inclusion of a viscoelastic memory term in our
equations, has received very little attention in the mathematical literature. Due to the unusual form
of the moving-boundary condition, further study is needed as to the existence and uniqueness of
solutions satisfying such a condition. The moving boundary condition which results is not solvable
by similarity solutions, but can be solved by integral equation techniques. A solution process is
outlined to illustrate the unusual nature of the condition; the profiles which result are characteristic
of a dissolving polymer
