Rocky Mountain Journal of Mathematics

Blow-up of multi-componential solutions in heat equations with exponential boundary flux

Fengjie Li, Shimei Zheng, and Bingchen Liu

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Abstract

This paper deals with heat equations coupled via exponential boundary flux, where the solution is made up of $n$ components. Under certain monotone assumptions, necessary and sufficient conditions are obtained for simultaneous blow-up of at least two components for each initial datum. As for two components blowing up simultaneously, it is interesting that the representations of blow-up rates are quite different with respect to the different blow-up mechanisms and positions between the two components.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 7 (2017), 2295-2321.

Dates
First available in Project Euclid: 24 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1514084429

Digital Object Identifier
doi:10.1216/RMJ-2017-47-7-2295

Mathematical Reviews number (MathSciNet)
MR3748232

Zentralblatt MATH identifier
06828641

Subjects
Primary: 35B33: Critical exponents 35B40: Asymptotic behavior of solutions 35K05: Heat equation 35K60: Nonlinear initial value problems for linear parabolic equations

Keywords
Non-simultaneous blow-up blow-up rate blow-up set

Citation

Li, Fengjie; Zheng, Shimei; Liu, Bingchen. Blow-up of multi-componential solutions in heat equations with exponential boundary flux. Rocky Mountain J. Math. 47 (2017), no. 7, 2295--2321. doi:10.1216/RMJ-2017-47-7-2295. https://projecteuclid.org/euclid.rmjm/1514084429


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