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Theorem on the existence of solutions of quasi-static moving boundary problems

Published online by Cambridge University Press:  26 September 2008

Bart Klein Obbink
Bart Klein Obbink
Affiliation:
Department of Mathematics and Computational Science, Eindhoven University of Technology, P. O. Box 513, Eindhoven, The Netherlands (e-mail: bartk@win.tue.nl)
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Abstract

Using the theory of conformal mappings, we show that two-dimensional quasi-static moving boundary problems can be described by a non-linear Löwner-Kufarev equation and a functional relation ℱ between the shape of the boundary and the velocity at the boundary. Together with the initial data, this leads to an initial value problem. Assuming that ℱ satisfies certain conditions, we prove a theorem stating that this initial value problem has a local solution in time. The proof is based on some straightforward estimates on solutions of Löwner-Kufarev equations and an iteration technique.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 5 , October 1995 , pp. 529 - 538
Copyright
Copyright © Cambridge University Press 1995

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