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An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems

D. A. Edwards and D. S. Cohen
SIAM Journal on Applied Mathematics
Vol. 55, No. 3 (Jun., 1995), pp. 662-676
Stable URL: http://www.jstor.org/stable/2102541
Page Count: 15
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An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems
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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.

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