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Changing Time History in Moving Boundary Problems

Cohen, Donald S. and Erneux, Thomas (1990) Changing Time History in Moving Boundary Problems. SIAM Journal on Applied Mathematics, 50 (2). pp. 483-489. ISSN 0036-1399. doi:10.1137/0150028.

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A class of diffusion-stress equations modeling transport of solvent in glassy polymers is considered. The problem is formulated as a one-phase Stefan problem. It is shown that the moving front changes like √t initially but quickly behaves like t as t increases. The behavior is typical of stress-dominated transport. The quasi-steady state approximation is used to analyze the time history of the moving front. This analysis is motivated by the small time solution.

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Additional Information:©1990 Society for Industrial and Applied Mathematics. Received by the editors June 12, 1989; accepted for publication (in revised form) July 25, 1989. This paper is dedicated to Edward L. Reiss on the occasion of his 60th birthday. [D.S.C.] was supported in part by the United States Army Research Office (Durham), Contract DAAL03-89-K-0014, National Science Foundation grant DMS-88706642, and Air Force Office of Scientific Research grant AFOSR-88-0269. [T.E.] was supported in part by National Science Foundation grant DMS-8701302 and United States Air Force Office of Scientific Research grant AFOSR 85-0150.
Funding AgencyGrant Number
Army Research OfficeDAAL03-89-K-0014
National Science FoundationDMS-88706642
Air Force Office of Scientific ResearchAFOSR-88-0269
National Science FoundationDMS-8701302
Air Force Office of Scientific ResearchAFOSR 85-0150
Subject Keywords:one phase Stefan problem; diffusion in polymers
Issue or Number:2
Record Number:CaltechAUTHORS:COHsiamjam90
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12831
Deposited On:12 Jan 2009 20:16
Last Modified:08 Nov 2021 22:33

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