On the Parabolicity of the Muskat Problem: Well-Posedness, Fingering, and Stability Results
Open Access
- 3 April 2011
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Zeitschrift für Analysis und ihre Anwendungen
- Vol. 30 (2) , 193-218
- https://doi.org/10.4171/zaa/1431
Abstract
We study the Muskat problem in a periodic geometry and incorporate capillary as well as gravity effects in the modelling. The problem is rewritten as an abstract evolution equation. By analysing this evolution equation we prove wellposedness of the problem and we establish exponential stability of some flat equilibrium. Using bifurcation theory we also find finger shaped steady-states which are all unstable.Keywords
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