Mathematics > Analysis of PDEs
[Submitted on 14 May 2010 (v1), last revised 21 Sep 2011 (this version, v2)]
Title:On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results
View PDFAbstract: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.
Submission history
From: Bogdan-Vasile Matioc [view email][v1] Fri, 14 May 2010 12:40:47 UTC (152 KB)
[v2] Wed, 21 Sep 2011 11:16:43 UTC (153 KB)
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