Self-similarity in a thin film Muskat problem
  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. 
Philippe Laurencot (IMT), Bogdan-Vasile Matioc (IFAM)
math.AP