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Zeitschrift für Analysis und ihre Anwendungen


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Volume 30, Issue 2, 2011, pp. 193–218
DOI: 10.4171/ZAA/1431

Published online: 2011-04-03

On the Parabolicity of the Muskat Problem: Well-Posedness, Fingering, and Stability Results

Joachim Escher[1] and Bogdan-Vasile Matioc[2]

(1) University of Hannover, Germany
(2) Leibniz University Hannover, Germany

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: Classical solution, steady-state solutions, stability

Escher Joachim, Matioc Bogdan-Vasile: On the Parabolicity of the Muskat Problem: Well-Posedness, Fingering, and Stability Results. Z. Anal. Anwend. 30 (2011), 193-218. doi: 10.4171/ZAA/1431