Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients

This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis based on variational techniques particular gradient flows space probability measures equipped distance arising Monge–Kantorovich optimal transport problem. The associated internal energy functionals general fail be differentiable, therefore classical results do not apply directly our setting. We combination both linear porous medium type diffusions we show existence uniqueness solutions sense distributions suitable Sobolev spaces. notion solution allows us give a fine characterization emerging critical regions, observed previously numerical experiments. A link three phase free boundary problem also pointed out.