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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 643819, 5 pages
Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary Conditions
1Department of Mathematics, Dalian Nationalities University, Dalian 116600, China
2School of Science, East China Institute of Technology, Nanchang 330013, China
3School of Science, Dalian Jiaotong University, Dalian 116028, China
Received 4 April 2013; Accepted 4 June 2013
Academic Editor: Daniel C. Biles
Copyright © 2013 Chengyuan Qu and Bo 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.
- C. Budd, B. Dold, and A. Stuart, “Blowup in a partial differential equation with conserved first integral,” SIAM Journal on Applied Mathematics, vol. 53, no. 3, pp. 718–742, 1993.
- B. Hu and H.-M. Yin, “Semilinear parabolic equations with prescribed energy,” Rendiconti del Circolo Matematico di Palermo. Serie II, vol. 44, no. 3, pp. 479–505, 1995.
- N. D. Alikakos and L. C. Evans, “Continuity of the gradient for weak solutions of a degenerate parabolic equation,” Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol. 62, no. 3, pp. 253–268, 1983.
- M. Jazar and R. Kiwan, “Blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 25, no. 2, pp. 215–218, 2008.
- A. El Soufi, M. Jazar, and R. Monneau, “A gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 24, no. 1, pp. 17–39, 2007.
- C. Y. Qu, X. L. Bai, and S. N. Zheng, “Blow-up and extinction in a nonlocal -Laplace equation with Neumann boundary conditions,” Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol. 25, no. 2, pp. 215–218, 2008.
- H. Fujita, “On the blowing up of solutions of the Cauchy problem for ,” Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics, vol. 13, pp. 109–124, 1966.
- K. Deng and H. A. Levine, “The role of critical exponents in blow-up theorems: the sequel,” Journal of Mathematical Analysis and Applications, vol. 243, no. 1, pp. 85–126, 2000.
- Y. X. Li and C. H. Xie, “Blow-up for -Laplace parabolic equations,” Electronic Journal of Differential Equations, vol. 2003, pp. 1–12, 2005.
- J. N. Zhao, “Existence and nonexistence of solutions for ,” Journal of Mathematical Analysis and Applications, vol. 172, no. 1, pp. 130–146, 1993.
- S. Zheng, X. Song, and Z. Jiang, “Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux,” Journal of Mathematical Analysis and Applications, vol. 298, no. 1, pp. 308–324, 2004.
- W. Gao and Y. Han, “Blow-up of a nonlocal semilinear parabolic equation with positive initial energy,” Applied Mathematics Letters, vol. 24, no. 5, pp. 784–788, 2011.
- E. Vitillaro, “Global nonexistence theorems for a class of evolution equations with dissipation,” Archive for Rational Mechanics and Analysis, vol. 149, no. 2, pp. 155–182, 1999.