Acta mathematica scientia, Series B >
UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE#br# NONLINEARITIES
Received date: 2010-10-05
Revised date: 2010-12-12
Online published: 2012-05-20
Supported by
Supported by the National Natural Science Founda-tion of China (10771024, 11171048) and the Education Department Program of Liaoning Province (L2010068).
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.
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 . DOI: 10.1016/S0252-9602(12)60085-X
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