Finite speed of propagation and waiting time for a thin film Muskat problem
Philippe Lauren\c{c}ot (IMT), Bogdan-Vasile Matioc (IFAM)
TL;DR
This paper proves finite speed of propagation for solutions to a thin film Muskat problem and identifies conditions for waiting time phenomena, enhancing understanding of the system's dynamics and support expansion behavior.
Contribution
It establishes finite speed of propagation and conditions for waiting time in a thin film Muskat problem, providing new insights into solution support dynamics.
Findings
Finite speed of propagation for solutions.
Conditions for waiting time phenomena.
Support expansion rate matches system scale invariance.
Abstract
Finite speed of propagation is established for non-negative weak solutions to a thin film approximation of the two-phase Muskat problem. The temporal 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.
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