The IPM equations model the motion of an incompressible fluid with variable density in a porous media and under the force of gravity. The Muskat problem deals with a situation in which the density of the fluid take two different and constant values. This problem is ill-posed in Sobolev's spaces for an unstable situation in which the part of the fluid with larger density is above. In this course we will present a construction of weak solution of the IPM equation which cosist of the mixing of the two densities for the Muskat problem. First of all we will introduce the technique of the convex integration applied to the IPM equations and after that we will go through the main steps to construct the mixing solutions.