- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- 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
International Journal of Differential Equations
Volume 2011 (2011), Article ID 751969, 9 pages
Spatial Profile of the Dead Core for the Fast Diffusion Equation with Dependent Coefficient
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
Received 7 May 2011; Accepted 25 October 2011
Academic Editor: Donal O'Regan
Copyright © 2011 Zhengce Zhang and Biao 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.
- J.-S. Guo and P. Souplet, “Fast rate of formation of dead-core for the heat equation with strong absorption and applications to fast blow-up,” Mathematische Annalen, vol. 331, no. 3, pp. 651–667, 2005.
- J.-S. Guo, C.-T. Ling, and P. Souplet, “Non-self-similar dead-core rate for the fast diffusion equation with strong absorption,” Nonlinearity, vol. 23, no. 3, pp. 657–673, 2010.
- V. A. Galaktionov, S. I. Shmarev, and J. L. Vazquez, “Regularity of interfaces in diffusion processes under the influence of strong absorption,” Archive for Rational Mechanics and Analysis, vol. 149, no. 3, pp. 183–212, 1999.
- Z. Zhang and B. Hu, “Rate estimates of gradient blowup for a heat equation with exponential nonlinearity,” Nonlinear Analysis, Theory, Methods & Applications, vol. 72, no. 12, pp. 4594–4601, 2010.
- Y. Li and P. Souplet, “Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains,” Communications in Mathematical Physics, vol. 293, no. 2, pp. 499–517, 2010.
- Z. Zhang and B. Hu, “Gradient blowup rate for a semilinear parabolic equation,” Discrete and Continuous Dynamical Systems Series A, vol. 26, no. 2, pp. 767–779, 2010.
- S. Zheng and X. Song, “Quenching rates for heat equations with coupled singular nonlinear boundary flux,” Science in China Series A, vol. 51, no. 9, pp. 1631–1643, 2008.
- J.-S. Guo and B. Hu, “Blowup rate estimates for the heat equation with a nonlinear gradient source term,” Discrete and Continuous Dynamical Systems Series A, vol. 20, no. 4, pp. 927–937, 2008.
- M. Winkler, “Infinite-time quenching in a fast diffusion equation with strong absorption,” Nonlinear Differential Equations and Applications, vol. 16, no. 1, pp. 41–61, 2009.
- W. Liu and M. Wang, “Blow-up of the solution for a p-Laplacian equation with positive initial energy,” Acta Applicandae Mathematicae, vol. 103, no. 2, pp. 141–146, 2008.
- J.-S. Guo and C.-C. Wu, “Finite time dead-core rate for the heat equation with a strong absorption,” The Tohoku Mathematical Journal, vol. 60, no. 1, pp. 37–70, 2008.