About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 746086, 7 pages
http://dx.doi.org/10.1155/2013/746086
Research Article

Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source

1School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
2School of Mathematical Sciences, Beijing Institute of Technology, Beijing 100081, China

Received 4 June 2013; Accepted 25 September 2013

Academic Editor: Julio Rossi

Copyright © 2013 Guosheng Zhang and Yifu Wang. 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. P. W. Bates and A. Chmaj, “An integrodifferential model for phase transitions: stationary solutions in higher space dimensions,” Journal of Statistical Physics, vol. 95, no. 5-6, pp. 1119–1139, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  2. P. W. Bates, P. C. Fife, X. Ren, and X. Wang, “Traveling waves in a convolution model for phase transitions,” Archive for Rational Mechanics and Analysis, vol. 138, no. 2, pp. 105–136, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  3. C. Carrillo and P. Fife, “Spatial effects in discrete generation population models,” Journal of Mathematical Biology, vol. 50, no. 2, pp. 161–188, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  4. X. Chen, “Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations,” Advances in Differential Equations, vol. 2, no. 1, pp. 125–160, 1997. View at MathSciNet
  5. J. Coville, J. Dávila, and S. Martínez, “Nonlocal anisotropic dispersal with monostable nonlinearity,” Journal of Differential Equations, vol. 244, no. 12, pp. 3080–3118, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  6. C. Cortázar, M. Elgueta, and J. D. Rossi, “Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions,” Israel Journal of Mathematics, vol. 170, pp. 53–60, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  7. P. Fife, “Some nonclassical trends in parabolic and parabolic-like evolutions,” in Trends in Nonlinear Analysis, pp. 153–191, Springer, Berlin, Germany, 2003. View at MathSciNet
  8. E. Chasseigne, M. Chaves, and J. D. Rossi, “Asymptotic behavior for nonlocal diffusion equations,” Journal de Mathématiques Pures et Appliquées, vol. 86, no. 3, pp. 271–291, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. L. Vázquez, The Porous Medium Equation, Oxford University Press, New York, NY, USA, 2007. View at MathSciNet
  10. V. A. Galaktionov, S. P. Kurdyumov, and A. A. Samarskiĭ, “A parabolic system of quasi-linear equations I,” Differential Equations, vol. 19, pp. 1558–1571, 1983. View at MathSciNet
  11. V. A. Galaktionov, S. P. Kurdyumov, and A. A. Samarskiĭ, “A parabolic system of quasilinear equations II,” Differential Equations, vol. 21, pp. 1049–1062, 1985. View at MathSciNet
  12. F. C. Li and C. H. Xie, “Global existence and blow-up for a nonlinear porous medium equation,” Applied Mathematics Letters, vol. 16, no. 2, pp. 185–192, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  13. C. Cortazar, M. Elgueta, and J. D. Rossi, “A nonlocal diffusion equation whose solutions develop a free boundary,” Annales Henri Poincaré, vol. 6, no. 2, pp. 269–281, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. Bogoya, R. Ferreira, and J. D. Rossi, “Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models,” Proceedings of the American Mathematical Society, vol. 135, no. 12, pp. 3837–3846, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  15. M. Bogoya and L. M. Elorreaga, “Problema de Dirichlet para una ecuación de difusión no local con fuente,” Boletín de Matemáticas, vol. 19, no. 1, pp. 55–64, 2012.