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

Boundary Value Problems volume 2007, Article number: 075258 (2007) Cite this article

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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References

  1. Pao CV: Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York, NY, USA; 1992:xvi+777.

    MATH  Google 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.

    Article  MATH  MathSciNet  Google Scholar 

  3. Du L, Yao Z-A: Note on non-simultaneous blow-up for a reaction-diffusion system. to appear in Applied Mathematics Letters

  4. Quirós F, Rossi JD: Non-simultaneous blow-up in a nonlinear parabolic system. Advanced Nonlinear Studies 2003,3(3):397–418.

    MATH  MathSciNet  Google Scholar 

  5. Deng K: Blow-up rates for parabolic systems. Zeitschrift für Angewandte Mathematik und Physik 1996,47(1):132–143. 10.1007/BF00917578

    Article  MATH  Google 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)00060-9

    Article  MATH  MathSciNet  Google 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/S0012-7094-97-08816-5

    Article  MATH  MathSciNet  Google 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. 10.2307/2154944

    Article  MATH  MathSciNet  Google Scholar 

  9. Lieberman GM: Second Order Parabolic Differential Equations. World Scientific, River Edge, NJ, USA; 1996:xii+439.

    Book  MATH  Google 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/s000330050060

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Jincheng College of Sichuan University, Chengdu, 611731, China

    Mingshu Fan

  2. Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China

    Lili Du

  3. School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China

    Lili Du

Authors
  1. Mingshu Fan
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  2. Lili Du
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Correspondence to Mingshu Fan.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Fan, M., Du, L. Simultaneous versus Nonsimultaneous Blowup for a System of Heat Equations Coupled Boundary Flux. Bound Value Probl 2007, 075258 (2007). https://doi.org/10.1155/2007/75258

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

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