Abstract
We prove existence, uniqueness, regularity results and estimates describing the behavior (both for large and small times) of a solution u of some nonlinear parabolic equations of Leray-Lions type including the p -Laplacian. In particular we show how the summability of the initial datum u 0 and the value of p influence the behavior of the solution u , producing ultracontractive or supercontractive estimates or extinction in finite time or different kinds of decay estimates.
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