Existence, uniqueness and behavior of solutions for a class of nonlinear parabolic problems

We prove existence, uniqueness, regularity results and estimates describing the behavior (both for large and small times) of a solution uu of some nonlinear parabolic equations of Leray-Lions type including the pp-Laplacian. In particular we show how the summability of the initial datum u0u0 and the value of pp influence the behavior of the solution uu, producing ultracontractive or supercontractive estimates or extinction in finite time or different kinds of decay estimates.