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Optimal estimates for blowup rate and behavior for nonlinear heat equations
Author(s) -
Merle Frank,
Zaag Hatem
Publication year - 1998
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199802)51:2<139::aid-cpa2>3.0.co;2-c
Subject(s) - mathematics , bounded function , nonlinear system , heat equation , space (punctuation) , mathematical analysis , pure mathematics , physics , computer science , quantum mechanics , operating system
We first describe all positive bounded solutions of ${\partial w \over \partial s} = \Delta w - {1 \over 2} y \cdot \nabla w - {w \over p - 1} + w^p$ where \input amstex \loadmsbm $(y,s)\in \Bbb R^N\times \Bbb R$ , 1 < p , and ( N − 2) p ≤ N + 2. We then obtain for blowup solutions u ( t ) of ${\partial u \over \partial t}=\Delta u +u^p$ uniform estimates at the blowup time and uniform space‐time comparison with solutions of u ′ = u p . © 1998 John Wiley & Sons, Inc.