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An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems

Edwards, D. A. and Cohen, D. S. (1995) An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems. SIAM Journal on Applied Mathematics, 55 (3). pp. 662-676. ISSN 0036-1399. doi:10.1137/S003613999325405X.

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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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Additional Information:© 1995 Society for Industrial and Applied Mathematics. Received by the editors August 18, 1993; accepted for publication May 10, 1994. This work was performed under United States Army Research Office (Durham) contract DAAL03-89-K-0014, National Science Foundation grant DMS-9024963, Air Force Office of Scientific Research grant AFOSR-91-0045, and Department of Energy grant W-7405-ENG-36 at the Center for Nonlinear Studies at Los Alamos. Additional support was provided by a National Science Foundation Graduate Fellowship. The authors wish to thank Thomas Witelski and Christopher Durning for their contributions, both direct and indirect, to this paper. Many of the calculations herein were performed using Maple.
Funding AgencyGrant Number
Army Research Office (ARO)DAAL03-89-K-0014
Air Force Office of Scientific Research (AFOSR)AFOSR-91-0045
Department of Energy (DOE)W-7405-ENG-36
NSF Graduate FellowshipUNSPECIFIED
Subject Keywords:integral equations, moving boundary-value problems, non-Fickian diffusion, polymer-penetrant systems
Issue or Number:3
Classification Code:AMS subject classifications: 35B25, 35C15, 35C20, 35K60, 35R35, 73F15, 76R99, 80A22
Record Number:CaltechAUTHORS:20120216-105409178
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Official Citation: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
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29338
Deposited By: Ruth Sustaita
Deposited On:16 Feb 2012 19:43
Last Modified:09 Nov 2021 17:06

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