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

Joachim Escher | Zendy; Bogdan–Vasile Matioc | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

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

Author(s) -

Joachim Escher,

Bogdan–Vasile Matioc

Publication year - 2011

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1431

Subject(s) - stability (learning theory) , bifurcation , mathematics , exponential stability , exponential function , mathematical analysis , exponential growth , statistical physics , physics , computer science , nonlinear system , quantum mechanics , machine learning

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. © European Mathematical Society

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research