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Abstract and Applied Analysis
Volume 2010, Article ID 680572, 12 pages
http://dx.doi.org/10.1155/2010/680572
Research Article

On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition

School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China

Received 9 June 2010; Accepted 15 September 2010

Academic Editor: Nicholas Alikakos

Copyright © 2010 Zhilei Liang. 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.

Linked References

  1. F. Quirós and J. D. Rossi, β€œBlow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions,” Indiana University Mathematics Journal, vol. 50, no. 1, pp. 629–654, 2001. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  2. A. A. Samarskii, V.A. Galaktionov, S. P. Kurdyumov, and A. P. Mikhailov, Blow-Up in Quasilinear Parabolic Equations, vol. 19 of de Gruyter Expositions in Mathematics, Walter de Gruyter, Berlin, Germany, 1995.
  3. Z. Wang, J. Yin, and C. Wang, β€œCritical exponents of the non-Newtonian polytropic filtration equation with nonlinear boundary condition,” Applied Mathematics Letters, vol. 20, no. 2, pp. 142–147, 2007. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  4. Z. Wu, J. Zhao, J. Yin, and H. Li, Nonlinear Diffusion Equations, World Scientific Publishing, River Edge, NJ, USA, 2001.
  5. V. A. Galaktionov and H. A. Levine, β€œOn critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary,” Israel Journal of Mathematics, vol. 94, pp. 125–146, 1996. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  6. B. H. Gilding and M. A. Herrero, β€œLocalization and blow-up of thermal waves in nonlinear heat conduction with peaking,” Mathematische Annalen, vol. 282, no. 2, pp. 223–242, 1988. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  7. M. C. Cortázar, M. Elgueta, and O. Venegas, β€œOn the blow-up set for ut=(um)xx,m>1, with nonlinear boundary conditions,” Monatshefte für Mathematik, vol. 142, no. 1-2, pp. 45–56, 2004. View at Publisher Β· View at Google Scholar Β· View at MathSciNet
  8. Z. Liang and J. Zhao, β€œLocalization for the evolution p-Laplacian equation with strongly nonlinear source term,” Journal of Differential Equations, vol. 246, no. 1, pp. 391–407, 2009. View at Publisher Β· View at Google Scholar