- 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 2012 (2012), Article ID 739156, 17 pages
On the Nonlinear Instability of Traveling Waves for a Sixth-Order Parabolic Equation
Department of Mathematics, Jilin University, Changchun 130012, China
Received 4 June 2012; Accepted 2 August 2012
Academic Editor: Ljubisa Kocinac
Copyright © 2012 Zhenbang Li and Changchun Liu. 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.
- T. V. Savina, A. A. Golovin, S. H. Davis, A. A. Nepomnyashchy, and P. W. Voorhees, “Faceting of a growing crystal surface by surface difusion,” Physical Review E, vol. 67, no. 2, part 1, Article ID 021606, 2003.
- J. W. Barrett, S. Langdon, and R. Nürnberg, “Finite element approximation of a sixth order nonlinear degenerate parabolic equation,” Numerische Mathematik, vol. 96, no. 3, pp. 401–434, 2004.
- J. D. Evans, V. A. Galaktionov, and J. R. King, “Unstable sixth-order thin film equation. I. Blow-up similarity solutions,” Nonlinearity, vol. 20, no. 8, pp. 1799–1841, 2007.
- J. D. Evans, V. A. Galaktionov, and J. R. King, “Unstable sixth-order thin film equation. II. Global similarity patterns,” Nonlinearity, vol. 20, no. 8, pp. 1843–1881, 2007.
- A. Jüngel and J.-P. Milišić, “A sixth-order nonlinear parabolic equation for quantum systems,” SIAM Journal on Mathematical Analysis, vol. 41, no. 4, pp. 1472–1490, 2009.
- C. Liu, “Qualitative properties for a sixth-order thin film equation,” Mathematical Modelling and Analysis, vol. 15, no. 4, pp. 457–471, 2010.
- C. Liu, “A sixth order degenerate equation with the higher order P-Laplacian operator,” Mathematica Slovaca, vol. 60, no. 6, pp. 847–864, 2010.
- M. D. Korzec, P. L. Evans, A. Münch, and B. Wagner, “Stationary solutions of driven fourth- and sixth-order Cahn-Hilliard-type equations,” SIAM Journal on Applied Mathematics, vol. 69, no. 2, pp. 348–374, 2008.
- E. A. Carlen, M. C. Carvalho, and E. Orlandi, “A simple proof of stability of fronts for the Cahn-Hilliard equation,” Communications in Mathematical Physics, vol. 224, no. 1, pp. 323–340, 2001.
- H. Gao and C. Liu, “Instability of traveling waves of the convective-diffusive Cahn-Hilliard equation,” Chaos, Solitons and Fractals, vol. 20, no. 2, pp. 253–258, 2004.
- S. A. Gourley and N. F. Britton, “Instability of travelling wave solutions of a population model with nonlocal effects,” IMA Journal of Applied Mathematics, vol. 51, no. 3, pp. 299–310, 1993.
- C. Liu, “Instability of traveling waves for a generalized diffusion model in population problems,” Electronic Journal of Qualitative Theory of Differential Equations, no. 18, pp. 1–10, 2004.
- J. Shatah and W. Strauss, “Spectral condition for instability,” in Contemporary Mathematics, vol. 255, pp. 189–198, 2000.
- W. Strauss and G. Wang, “Instability of traveling waves of the Kuramoto-Sivashinsky equation,” Chinese Annals of Mathematics B, vol. 23, no. 2, pp. 267–276, 2002.
- Q. Ye and Z. Li, Theory of Reaction-Diffusion Equations, Science Press, Beijing, China, 1994.
- M. Schechter, Spectra of Partial Differential Operators, American Elsevier, New York, NY, USA, 1971.