SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research Article

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

Mingshu Fan1* and Lili Du23

Author 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

For all author emails, please log on.

Boundary Value Problems 2007, 2007:075258  doi:10.1155/2007/75258

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/075258


Received:5 November 2006
Revisions received:18 January 2007
Accepted:23 March 2007
Published:20 May 2007

© 2007 Fan and Du

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.

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.

References

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

  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. 4(3), 523–536 (2005)

  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. 3(3), 397–418 (2003)

  5. Deng, K: Blow-up rates for parabolic systems. Zeitschrift für Angewandte Mathematik und Physik. 47(1), 132–143 (1996). PubMed Abstract | Publisher Full Text OpenURL

  6. Zhao, L, Zheng, S: Blow-up estimates for system of heat equations coupled via nonlinear boundary flux. Nonlinear Analysis. 54(2), 251–259 (2003). Publisher Full Text OpenURL

  7. Rial, DF, Rossi, JD: Blow-up results and localization of blow-up points in an -dimensional smooth domain. Duke Mathematical Journal. 88(2), 391–405 (1997). Publisher Full Text OpenURL

  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. 346(1), 117–135 (1994). Publisher Full Text OpenURL

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

  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. 48(5), 711–724 (1997). PubMed Abstract | Publisher Full Text OpenURL