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. (C) 2011 Elsevier Ltd. All rights reserved.
Existence, uniqueness and behavior of solutions for a class of nonlinear parabolic problems / Porzio, Maria Michaela. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 74:16(2011), pp. 5359-5382. [10.1016/j.na.2011.05.020]