UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE#br#
NONLINEARITIES

doi:10.1016/S0252-9602(12)60085-X

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 1126-1140.doi: 10.1016/S0252-9602(12)60085-X

UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE#br# NONLINEARITIES

孔令花^1,3|王金环^2,3|郑斯宁^3*

1. School of Science, Dalian Ocean University, Dalian 116023, China；
2. Department of Mathematics, Liaoning University, Shenyang 110036, China；
3. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

收稿日期:2010-10-05 修回日期:2010-12-12 出版日期:2012-05-20 发布日期:2012-05-20
通讯作者: 郑斯宁,snzheng@dlut.edu.cn E-mail:snzheng@dlut.edu.cn
基金资助:
Supported by the National Natural Science Founda-tion of China (10771024, 11171048) and the Education Department Program of Liaoning Province (L2010068).

UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE#br# NONLINEARITIES

KONG Ling-Hua^1,3, WANG Jin-Huan^2,3, ZHENG Si-Ning^3*

1. School of Science, Dalian Ocean University, Dalian 116023, China；
2. Department of Mathematics, Liaoning University, Shenyang 110036, China；
3. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received:2010-10-05 Revised:2010-12-12 Online:2012-05-20 Published:2012-05-20
Contact: ZHENG Si-Ning,snzheng@dlut.edu.cn E-mail:snzheng@dlut.edu.cn
Supported by:
Supported by the National Natural Science Founda-tion of China (10771024, 11171048) and the Education Department Program of Liaoning Province (L2010068).

摘要/Abstract

摘要：

This article deals with a nonlocal heat system subject to null Dirichlet bound-ary conditions, where the coupling nonlocal sources consist of mixed type asymmetric non-linearities. We at first give the criterion for simultaneous blow-up of solutions, and then establish the uniform blow-up profiles of solutions near the blow-up time. It is observed that not only the simultaneous blow-up rates of the two components u and v are asymmet-ric, but also the blow-up rates of the same component u (or v) may be in different levels under different dominations.

关键词: Heat systems, mixed type nonlinearity, uniform blow-up profiles, simulta-neous blow-up

Abstract:

Key words: Heat systems, mixed type nonlinearity, uniform blow-up profiles, simulta-neous blow-up

中图分类号:

35B40

孔令花, 王金环, 郑斯宁. UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE#br# NONLINEARITIES[J]. 数学物理学报(英文版), 2012, 32(3): 1126-1140.

KONG Ling-Hua, WANG Jin-Huan, ZHENG Si-Ning. UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE#br# NONLINEARITIES[J]. Acta mathematica scientia,Series B, 2012, 32(3): 1126-1140.

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UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE#br# NONLINEARITIES

UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE#br# NONLINEARITIES

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