  This paper shows finite time singularity formation for the Muskat problem in
a stable regime. The framework we found is with a dry region, where the density
and the viscosity are set equal to $0$ (the gradient of the pressure is equal
to $(0,0)$) in the complement of the fluid domain. The singularity is a
splash-type: a smooth fluid boundary collapses due to two different particles
evolve to collide at a single point. This is the first example of a splash
singularity for a parabolic problem.
