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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 414590, 24 pages
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.
- G. Gompper and J. Goos, “Fluctuating interfaces in microemulsion and sponge phases,” Physical Review E, vol. 50, no. 2, pp. 1325–1335, 1994.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- T. Dłotko, “Global attractor for the Cahn-Hilliard equation in and ,” Journal of Differential Equations, vol. 113, no. 2, pp. 381–393, 1994.
- 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.
- H. Wu and S. Zheng, “Global attractor for the 1-D thin film equation,” Asymptotic Analysis, vol. 51, no. 2, pp. 101–111, 2007.
- R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, vol. 68 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1988.
- 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.
- 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.