Local Existence And Uniqueness of Solutions of Degenerate Parabolic Equations

We consider a class of degenerate parabolic equaitons on a bounded domain with mixed boundary conditions. These problems arise, for example, in the study of flow through porous media. Under appropriate hypotheses, we establish the existence of a nonegative solution which is obtainable as a monotone limit of solutions of quasilinear parabolic equations. This construction is used establish uniqueness, cinparison, and L¹ continuous dependence theorems, as well some results on blow up of solutions in finite time