  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.
