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finite propagation speed

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Finite speed of propagation and waiting time for a thin-film Muskat problem
Part of
Philippe Laurençot, Bogdan-Vasile Matioc
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 4 / August 2017

Published online by Cambridge University Press:

05 July 2017, pp. 813-830

Print publication:

August 2017
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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.