An estimate of the localization for the evolution pp-Laplacian equation

Liang and Zhao showed in [Z. Liang, J. Zhao, Localization for the evolution pp-Laplacian equation with strongly nonlinear source term, J. Differential Equations 246 (2009) 391–407] that the unbounded solution of the equation ut=div(|∇u|p−2∇u)+uq,(x,t)∈RN×(0,T) is strictly localized for q≥p−1q≥p−1, provided that the initial function is compactly supported. In this work we give an upper estimate on the localization in terms of the initial support suppu0(x) and the blowing-up time T<∞T<∞.