Blow-up properties for heat equations coupled via different nonlinearities

This paper deals with heat equations coupled via exponential and power nonlinearities, subject to null Dirichlet boundary conditions. The complete and optimal classification on non-simultaneous and simultaneous blow-ups is proposed by four sufficient and necessary conditions. We find out that, in so...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 347; no. 1; pp. 294 - 303
Main Authors Liu, Bingchen, Li, Fengjie
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.11.2008
Elsevier
Subjects
Blow-up rate
Exact sciences and technology
Mathematical analysis
Mathematics
Non-simultaneous blow-up
Partial differential equations
Sciences and techniques of general use
Simultaneous blow-up
Simultaneous blow-up
Blow-up rate
Non-simultaneous blow-up
Solution blow up
Necessary condition
Sufficient condition
Heat equation
Mathematical analysis
Classification
Nonlinearity
Non-simultaneous blow-up;Simultaneous blow-up;Blow-up rate
Boundary condition
Application
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Summary:This paper deals with heat equations coupled via exponential and power nonlinearities, subject to null Dirichlet boundary conditions. The complete and optimal classification on non-simultaneous and simultaneous blow-ups is proposed by four sufficient and necessary conditions. We find out that, in some exponent region, the blow-up properties of the solutions depend much on the choosing of initial data. Moreover, all kinds of non-simultaneous and simultaneous blow-up rates are obtained.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.06.004