Localization for a doubly degenerate parabolic equation with strongly nonlinear sources

In this paper, we study the strict localization for the doubly degenerate parabolic equation with strongly nonlinear sources,\documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}${\partial}_tu={\rm{div}}(|\nabla u^m|^{p-2}\nabla u^m)+u^q, \quad p{>}2,m,q{>}1$\end{document}We prove that, for non‐negative compactly supported initial data, the strict localization occurs if and only if q ⩾ m ( p −1). Copyright © 2009 John Wiley & Sons, Ltd.