Self-similarity in a thin film Muskat problem

Philippe Laurencot (1) , Bogdan-Vasile Matioc (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IFAM - Institute for Applied Mathematics

The large time behavior of non-negative weak solutions to a thin film approximation of the two-phase Muskat problem is studied. A classification of self-similar solutions is first provided: there is always a unique even self-similar solution while a continuum of non-symmetric self-similar solutions exist for certain fluid configurations. Despite this non-uniqueness, convergence of all non-negative weak solutions towards a self-similar solution is proved.

Mots clés: thin film Muskat problem; degenerate parabolic system; self-similar solutions; asymptotic behavior

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Laurencot, Bogdan-Vasile Matioc. Self-similarity in a thin film Muskat problem. SIAM Journal on Mathematical Analysis, 2017, 49 (4), pp.2790--2842. ⟨hal-01068150⟩