An estimate of the localization for the evolution -Laplacian equation

Liang and Zhao showed in [Z. Liang, J. Zhao, Localization for the evolution p -Laplacian equation with strongly nonlinear source term, J. Differential Equations 246 (2009) 391–407] that the unbounded solution of the equation u t = div ( | ∇ u | p − 2 ∇ u ) + u q , ( x , t ) ∈ R N × ( 0 , T ) is strictly localized for q ≥ 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 supp u 0 ( x ) and the blowing-up time T < ∞ .