An unusual moving boundary condition arising in anomalous diffusion problems. (English) Zbl 0839.35148
Summary: 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 robbery 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.
MSC:
35R35 | Free boundary problems for PDEs |
35B25 | Singular perturbations in context of PDEs |
35C15 | Integral representations of solutions to PDEs |
35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
74Hxx | Dynamical problems in solid mechanics |
80A22 | Stefan problems, phase changes, etc. |
82D60 | Statistical mechanics of polymers |