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arXiv · 1005.2512

On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results

Joachim Escher·Bogdan-Vasile Matioc
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Abstract

We consider in this paper the Muskat problem in a periodic geometry and incorporate capillary as well as gravity effects in the modelling. The problem re-writes as an abstract evolution equation and we use this property to prove well-posedness of the problem and to establish exponential stability of some flat equilibrium. Using bifurcation theory we also find finger shaped steady-states which are all unstable.

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Joachim Escher, Bogdan-Vasile Matioc. 2010-05-14. On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results. https://arxiv.org/abs/1005.2512

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