Determination of the blow-up rate for the semilinear wave equation

被引：77
作者：
Merle, F
Zaag, H
机构：
[1] Univ Cergy Pontoise, Dept Math, F-95302 Cergy Pontoise, France
[2] Ecole Normale Super, Dept Math & Applicat, CNRS, UMR 8553, F-75005 Paris, France
来源：
AMERICAN JOURNAL OF MATHEMATICS | 2003年 / 125卷 / 05期
关键词：
D O I：
10.1353/ajm.2003.0033
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we find the optimal blow-up rate for the semilinear wave equation with a power nonlinearity. The exponent p is superlinear and less than 1 + (4)/(N-1) if N greater than or equal to 2.
引用
收藏
页码：1147 / 1164
页数：18
相关论文
共 13 条
[1]  
Alinhac S., 1995, BLOWUP NONLINEAR HYP, V17
[2]  
Antonini C, 2001, INT MATH RES NOTICES, V2001, P1141
[3]   THE BLOW-UP BOUNDARY FOR NONLINEAR-WAVE EQUATIONS [J].
CAFFARELLI, LA ;
FRIEDMAN, A .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 297 (01) :223-241
[4]   GLOBAL AND LOCAL BEHAVIOR OF POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS [J].
GIDAS, B ;
SPRUCK, J .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1981, 34 (04) :525-598
[5]   NONDEGENERACY OF BLOWUP FOR SEMILINEAR HEAT-EQUATIONS [J].
GIGA, Y ;
KOHN, RV .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (06) :845-884
[6]  
GIGA Y, 2003, BLOW RATE SEMILINEAR
[7]   CLASS OF NON-LINEAR SCHRODINGER EQUATIONS .2. SCATTERING THEORY, GENERAL-CASE [J].
GINIBRE, J ;
VELO, G .
JOURNAL OF FUNCTIONAL ANALYSIS, 1979, 32 (01) :33-71
[8]   BLOW-UP OF SOLUTIONS OF NON-LINEAR WAVE-EQUATIONS IN 3 SPACE DIMENSIONS [J].
JOHN, F .
MANUSCRIPTA MATHEMATICA, 1979, 28 (1-3) :235-268
[9]   BLOW-UP SURFACES FOR NONLINEAR-WAVE EQUATIONS .1. [J].
KICHENASSAMY, S ;
LITTMAN, W .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (3-4) :431-452
[10]   BLOW-UP SURFACES FOR NONLINEAR-WAVE EQUATIONS .2. [J].
KICHENASSAMY, S ;
LITTMAN, W .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (11) :1869-1899
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