  We construct mixing solutions to the incompressible porous media equation
starting from Muskat type data in the partially unstable regime. In particular,
we consider bubble and turned type interfaces with Sobolev regularity. As a
by-product, we prove the continuation of the evolution of IPM after the
Rayleigh-Taylor and smoothness breakdown exhibited in [18,17]. At each time
slice the space is split into three evolving domains: two non-mixing zones and
a mixing zone which is localized in a neighborhood of the unstable region. In
this way, we show the compatibility between the classical Muskat problem and
the convex integration method.
