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Finite speed of propagation and waiting time for a thin-film Muskat problem

Part of: Parabolic equations and systems Equations of mathematical physics and other areas of application Partial differential equations

Published online by Cambridge University Press:  05 July 2017

Philippe Laurençot  and
Bogdan-Vasile Matioc
Philippe Laurençot
Affiliation:
Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, 31062 Toulouse CEDEX 9, France (laurenco@math.univ-toulouse.fr)
Bogdan-Vasile Matioc
Affiliation:
Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany (matioc@ifam.uni-hannover.de)
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Extract

Propagation at a finite speed is established for non-negative weak solutions to a thin-film approximation of the two-phase Muskat problem. The expansion rate of the support matches the scale invariance of the system. Moreover, we determine sufficient conditions on the initial data for the occurrence of waiting time phenomena.

Keywords

finite propagation speedwaiting timedegenerate parabolic system

MSC classification

Secondary: 35K65: Degenerate parabolic equations 35K40: Second-order parabolic systems 35B99: None of the above, but in this section 35Q35: PDEs in connection with fluid mechanics
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 4 , August 2017 , pp. 813 - 830
Copyright
Copyright © Royal Society of Edinburgh 2017 

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