A complete upper estimate on the localization for the degenerate parabolic equation with nonlinear source

Abstract This paper deals with the Cauchy problem for the degenerate parabolic equation with a strongly nonlinear source urn:x-wiley:1704214:media:mma3094:mma3094-math-0001 where N ≥ 1, p > 2, q ≥ p − 1, and the blow‐up time T < ∞ . It has been shown that the solution u ( x , t ) is strictly localized for q ≥ p − 1, provided that the initial function u 0 ( x ) has a compact support by Liang and Zhao. In addition, if q > 2 p − 1, an upper estimate on the localization in terms of the initial support and the blow‐up time T is partially derived by Liang. In this work, by using the De Giorgi‐type iteration technique, we give a complete estimate on the localization for all q ≥ p − 1. Copyright © 2014 John Wiley & Sons, Ltd.

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