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Localization for a doubly degenerate parabolic equation with strongly nonlinear sources
Author(s) -
Xiang Zhaoyin
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1236
Subject(s) - degenerate energy levels , mathematics , nonlinear system , parabolic partial differential equation , mathematical analysis , mathematical physics , partial differential equation , physics , quantum mechanics
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.