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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 746086, 7 pages
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.
- 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.
- 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.
- C. Carrillo and P. Fife, “Spatial effects in discrete generation population models,” Journal of Mathematical Biology, vol. 50, no. 2, pp. 161–188, 2005.
- 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.
- 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.
- 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.
- P. Fife, “Some nonclassical trends in parabolic and parabolic-like evolutions,” in Trends in Nonlinear Analysis, pp. 153–191, Springer, Berlin, Germany, 2003.
- 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.
- J. L. Vázquez, The Porous Medium Equation, Oxford University Press, New York, NY, USA, 2007.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.