  We consider a simplified model of a two-phase flow through a heterogeneous
porous medium, in which the convection is neglected. This leads to a nonlinear
degenerate parabolic problem in a domain shared in an arbitrary finite number
of homogeneous porous media. We introduce a new way to connect capillary
pressures on the interfaces between the homogeneous domains, which leads to a
general notion of solution. We then compare this notion of solution with an
existing one, showing that it allows to deal with a larger class of problems.
We prove the existence of such a solution in a general case, then we prove the
existence and the uniqueness of a regular solution in the one-dimensional case
for regular enough initial data.
