THE PROFILE NEAR BLOWUP TIME FOR SOLUTION OF THE HEAT-EQUATION WITH A NONLINEAR BOUNDARY-CONDITION

被引：199
作者：
HU, B
YIN, HM
机构：
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 346卷 / 01期
关键词：
BLOWUP RATE; ASYMPTOTIC BEHAVIOR; ELLIPTIC ESTIMATES; PARABOLIC ESTIMATES;
D O I：
10.2307/2154944
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper studies the blowup profile near the blowup time for the heat equation u(t) = DELTAu with the nonlinear boundary condition u(n) = u(p) on partial derivativeOMEGA x [0, T). Under certain assumptions, the exact rate of the blowup is established. It is also proved that the blowup will not occur in the interiror of the domain. The asymptotic behavior near the blowup point is also studied.
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页码：117 / 135
页数：19
相关论文
共 27 条
[1]   PARABOLIC EVOLUTION-EQUATIONS AND NONLINEAR BOUNDARY-CONDITIONS [J].
AMANN, H .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1988, 72 (02) :201-269
[2]  
Bebernes J., 1989, MATH PROBLEMS COMBUS, V83
[3]   ASYMPTOTIC SYMMETRY AND LOCAL BEHAVIOR OF SEMILINEAR ELLIPTIC-EQUATIONS WITH CRITICAL SOBOLEV GROWTH [J].
CAFFARELLI, LA ;
GIDAS, B ;
SPRUCK, J .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (03) :271-297
[4]   BLOW-UP OF SOLUTIONS OF NONLINEAR HEAT-EQUATIONS [J].
CAFFARRELLI, LA ;
FRIEDMAN, A .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1988, 129 (02) :409-419
[5]  
CHADAM JM, 1993, P EDINBURGH MATH SOC, V37, P101
[6]  
Chipot M., 1991, ACTA MATH U COMENIAN, V60, P35
[7]   THE BLOW-UP RATE FOR THE HEAT-EQUATION WITH A NONLINEAR BOUNDARY-CONDITION [J].
FILA, M ;
QUITTNER, P .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1991, 14 (03) :197-205
[8]  
Fila M., 1989, COMMENT MATH UNIV CA, V30, P479
[9]   BLOW-UP OF POSITIVE SOLUTIONS OF SEMILINEAR HEAT-EQUATIONS [J].
FRIEDMAN, A ;
MCLEOD, B .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1985, 34 (02) :425-447
[10]  
Friedman A., 1983, PARTIAL DIFFERENTIAL
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