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  • Research Article
  • Open Access

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

Boundary Value Problems20072007:075258

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

  • Received: 5 November 2006
  • Accepted: 23 March 2007
  • Published:

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.

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Heat Equation

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Authors’ Affiliations

(1)
Department of Mathematics, Jincheng College of Sichuan University, Chengdu, 611731, China
(2)
Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China
(3)
School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China

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

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