Boundary Value Problems

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Simultaneous versus Nonsimultaneous Blowup for a System of Heat Equations Coupled Boundary Flux

Boundary Value Problems20072007:075258

https://doi.org/10.1155/2007/75258

©  M. Fan and L. Du 2007

Received: 5 November 2006

Accepted: 23 March 2007

Published: 20 May 2007

Abstract

This paper deals with a semilinear parabolic system in a bounded interval, completely coupled at the boundary with exponential type. We characterize completely the range of parameters for which nonsimultaneous and simultaneous blowup occur.

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Authors’ Affiliations

(1)
Department of Mathematics, Jincheng College of Sichuan University
(2)
Department of Mathematics, Sun Yat-Sen University
(3)
School of Mathematical Sciences, South China University of Technology

References

  1. Pao CV: Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York, NY, USA; 1992:xvi+777.MATHGoogle Scholar
  2. Brändle C, Quirós F, Rossi JD: Non-simultaneous blow-up for a quasilinear parabolic system with reaction at the boundary. Communications on Pure and Applied Analysis 2005,4(3):523–536.MATHMathSciNetView ArticleGoogle Scholar
  3. Du L, Yao Z-A: Note on non-simultaneous blow-up for a reaction-diffusion system. to appear in Applied Mathematics LettersGoogle Scholar
  4. Quirós F, Rossi JD: Non-simultaneous blow-up in a nonlinear parabolic system. Advanced Nonlinear Studies 2003,3(3):397–418.MATHMathSciNetGoogle Scholar
  5. Deng K: Blow-up rates for parabolic systems. Zeitschrift für Angewandte Mathematik und Physik 1996,47(1):132–143. 10.1007/BF00917578MATHView ArticleGoogle Scholar
  6. Zhao L, Zheng S: Blow-up estimates for system of heat equations coupled via nonlinear boundary flux. Nonlinear Analysis 2003,54(2):251–259. 10.1016/S0362-546X(03)00060-9MATHMathSciNetView ArticleGoogle Scholar
  7. Rial DF, Rossi JD: Blow-up results and localization of blow-up points in an-dimensional smooth domain. Duke Mathematical Journal 1997,88(2):391–405. 10.1215/S0012-7094-97-08816-5MATHMathSciNetView ArticleGoogle Scholar
  8. Hu B, Yin H-M: The profile near blow-up time for solution of the heat equation with a nonlinear boundary condition. Transactions of the American Mathematical Society 1994,346(1):117–135. 10.2307/2154944MATHMathSciNetView ArticleGoogle Scholar
  9. Lieberman GM: Second Order Parabolic Differential Equations. World Scientific, River Edge, NJ, USA; 1996:xii+439.MATHView ArticleGoogle Scholar
  10. Acosta G, Rossi JD: Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition. Zeitschrift für Angewandte Mathematik und Physik 1997,48(5):711–724. 10.1007/s000330050060MATHMathSciNetView ArticleGoogle Scholar

Copyright

© M. Fan and L. Du 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.