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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 414590, 24 pages
doi:10.1155/2012/414590
Research Article
Some Properties of Solutions for the Sixth-Order Cahn-Hilliard-Type Equation
Department of Mathematics, Jilin University, Changchun 130012, China
Received 10 July 2012; Revised 18 August 2012; Accepted 6 September 2012
Academic Editor: Ruediger Landes
Copyright © 2012 Zhao Wang 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.
Linked References
- G. Gompper and J. Goos, “Fluctuating interfaces in microemulsion and sponge phases,” Physical Review E, vol. 50, no. 2, pp. 1325–1335, 1994. View at Publisher · View at Google Scholar · View at Scopus
- G. Gompper and M. Kraus, “Ginzburg-Landau theory of ternary amphiphilic systems. I. Gaussian interface fluctuations,” Physical Review E, vol. 47, no. 6, pp. 4289–4300, 1993. View at Publisher · View at Google Scholar · View at Scopus
- G. Gompper and M. Kraus, “Ginzburg-Landau theory of ternary amphiphilic systems. II. Monte Carlo simulations,” Physical Review E, vol. 47, no. 6, pp. 4301–4312, 1993. View at Publisher · View at Google Scholar · View at Scopus
- 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- Z. Li and C. Liu, “On the nonlinear instability of travelingwaves for a sixth order parabolic equation,” Abstract and Applied Analysis, vol. 2012, Article ID 739156, 17 pages, 2012. View at Publisher · View at Google Scholar
- 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 and Y. Tian, “Weak solutions for a sixth-order thin film equation,” The Rocky Mountain Journal of Mathematics, vol. 41, no. 5, pp. 1547–1565, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- I. Pawłow and W. M. Zajączkowski, “A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures,” Communications on Pure and Applied Analysis, vol. 10, no. 6, pp. 1823–1847, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- G. Schimperna and I. Pawłow, “On a class of Cahn-Hilliard models with nonlinear diffusion,” http://arxiv.org/abs/1106.1581.
- C. Liu, “Regularity of solutions for a sixth order nonlinear parabolic equation in two spacedimensions,” Annales Polonici Mathematici. In press.
- 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- B. Nicolaenko, B. Scheurer, and R. Temam, “Some global dynamical properties of a class of pattern formation equations,” Communications in Partial Differential Equations, vol. 14, no. 2, pp. 245–297, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- T. Dłotko, “Global attractor for the Cahn-Hilliard equation in and ,” Journal of Differential Equations, vol. 113, no. 2, pp. 381–393, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- D. Li and C. Zhong, “Global attractor for the Cahn-Hilliard system with fast growing nonlinearity,” Journal of Differential Equations, vol. 149, no. 2, pp. 191–210, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- H. Wu and S. Zheng, “Global attractor for the 1-D thin film equation,” Asymptotic Analysis, vol. 51, no. 2, pp. 101–111, 2007. View at Zentralblatt MATH
- R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, vol. 68 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1988. View at Publisher · View at Google Scholar
- A. Pazy, “Semigroups of linear operators and applications to partial differential equations,” in Applied Mathematical Sciences, vol. 44, Springer, 1983.
- L. Song, Y. Zhang, and T. Ma, “Global attractor of the Cahn-Hilliard equation in spaces,” Journal of Mathematical Analysis and Applications, vol. 355, no. 1, pp. 53–62, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- L. Song, Y. Zhang, and T. Ma, “Global attractor of a modified Swift-Hohenberg equation in spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 1, pp. 183–191, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH