Skip to main content


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

Article metrics

  • 975 Accesses

  • 1 Citations


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.



  1. 1.

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

  2. 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.

  3. 3.

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

  4. 4.

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

  5. 5.

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

  6. 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

  7. 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

  8. 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

  9. 9.

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

  10. 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

Download references

Author information

Correspondence to Mingshu Fan.

Rights and permissions

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

Reprints and Permissions

About this article


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