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A 2-D free boundary problem with onset of a phase and singular elliptic boundary value problems

A 2-D free boundary problem with onset of a phase and singular elliptic boundary value problems Numerous models of industrial processes, such as diffusion in glassy polymers or solidification phenomena, lead to general one phase free boundary value problems with phase onset.The classical well-posedness of a fast diffusion approximation to the concerned free boundary value problems is proved. The analysis is performed via a singular change of variables leading to a singular system in a fixed domain. An existence and regularity theory for classical solutions is developed for the relevant underlying class of singular elliptic boundary value problems and is then used to prove the well-posedness for the models considered in which these are coupled to Hamilton-Jacobi or to parabolic evolution equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

A 2-D free boundary problem with onset of a phase and singular elliptic boundary value problems

Guidotti, Patrick
Journal of Evolution Equations , Volume 2 (4) – Nov 1, 2002
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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2002 by Birkhäuser Verlag Basel,
Subject
Mathematics; Analysis
ISSN
1424-3199
DOI
10.1007/PL00012596
Publisher site
See Article on Publisher Site

Abstract

Numerous models of industrial processes, such as diffusion in glassy polymers or solidification phenomena, lead to general one phase free boundary value problems with phase onset.The classical well-posedness of a fast diffusion approximation to the concerned free boundary value problems is proved. The analysis is performed via a singular change of variables leading to a singular system in a fixed domain. An existence and regularity theory for classical solutions is developed for the relevant underlying class of singular elliptic boundary value problems and is then used to prove the well-posedness for the models considered in which these are coupled to Hamilton-Jacobi or to parabolic evolution equations.

Journal

Journal of Evolution Equations – Springer Journals

Published: Nov 1, 2002

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