JournalszaaVol. 30, No. 2pp. 193–218

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

  • Joachim Escher

    University of Hannover, Germany
  • Bogdan-Vasile Matioc

    Leibniz University Hannover, Germany
On the Parabolicity of the Muskat Problem: Well-Posedness, Fingering, and Stability Results cover
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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.

Cite this article

Joachim Escher, Bogdan-Vasile Matioc, On the Parabolicity of the Muskat Problem: Well-Posedness, Fingering, and Stability Results. Z. Anal. Anwend. 30 (2011), no. 2, pp. 193–218

DOI 10.4171/ZAA/1431