- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 747613, 5 pages
Extinction and Nonextinction for the Fast Diffusion Equation
1College of Mathematics and Physics, Chongqing University, Chongqing 400044, China
2College of Elementary Education, Chongqing Normal University, Chongqing 400047, China
3School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
Received 28 February 2013; Accepted 28 April 2013
Academic Editor: Ru Dong Chen
Copyright © 2013 Chunlai Mu et al. 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.
- A. S. Kalashnikov, “The nature of the propagation of perturbations in problems of nonlinear heat conduction with absorption,” USSR Computational Mathematics and Mathematical Physics, vol. 14, no. 4, pp. 70–85, 1974.
- Y. G. Gu, “Necessary and sufficient conditions for extinction of solutions to parabolic equations,” Acta Mathematica Sinica, vol. 37, no. 1, pp. 73–79, 1994 (Chinese).
- E. Dibenedetto, Degenerate Parabolic Equations, Springer, New York, NY, USA, 1993.
- L. C. Evans and B. F. Knerr, “Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities,” Illinois Journal of Mathematics, vol. 23, no. 1, pp. 153–166, 1979.
- A. Friedman and M. A. Herrero, “Extinction properties of semilinear heat equations with strong absorption,” Journal of Mathematical Analysis and Applications, vol. 124, no. 2, pp. 530–546, 1987.
- V. A. Galaktionov and J. L. Vazquez, “Continuation of blowup solutions of nonlinear heat equations in several space dimensions,” Communications on Pure and Applied Mathematics, vol. 50, no. 1, pp. 1–67, 1997.
- M. A. Herrero and J. J. L. Velázquez, “Approaching an extinction point in one-dimensional semilinear heat equations with strong absorption,” Journal of Mathematical Analysis and Applications, vol. 170, no. 2, pp. 353–381, 1992.
- S. Benachour, Ph. Laurençot, and D. Schmitt, “Extinction and decay estimates for viscous Hamilton-Jacobi equations in RN,” Proceedings of the American Mathematical Society, vol. 130, no. 4, pp. 1103–1111, 2002.
- S. Benachour, Ph. Laurençot, D. Schmitt, and Ph. Souplet, “Extinction and non-extinction for viscous Hamilton-Jacobi equations in RN,” Asymptotic Analysis, vol. 31, no. 3-4, pp. 229–246, 2002.
- Y. Li and J. Wu, “Extinction for fast diffusion equations with nonlinear sources,” Electronic Journal of Differential Equations, vol. 2005, no. 23, pp. 1–7, 2005.
- Y. Tian and C. Mu, “Extinction and non-extinction for a p-Laplacian equation with nonlinear source,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 69, no. 8, pp. 2422–2431, 2008.
- W. Liu and B. Wu, “A note on extinction for fast diffusive p-Laplacian with sources,” Mathematical Methods in the Applied Sciences, vol. 31, no. 12, pp. 1383–1386, 2008.
- J. Yin and C. Jin, “Critical extinction and blow-up exponents for fast diffusive p-Laplacian with sources,” Mathematical Methods in the Applied Sciences, vol. 30, no. 10, pp. 1147–1167, 2007.
- A. W. Leung and Q. Zhang, “Finite extinction time for nonlinear parabolic equations with nonlinear mixed boundary data,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 31, no. 1-2, pp. 1–13, 1998.