Abstract and Applied Analysis

Weak Solutions for a Sixth Order Cahn-Hilliard Type Equation with Degenerate Mobility

Aibo Liu and Changchun Liu

Full-text: Open access

Abstract

We study an initial-boundary problem for a sixth order Cahn-Hilliard type equation, which arises in oil-water-surfactant mixtures. An existence result for the problem with a concentration dependent diffusional mobility in three space dimensions is presented.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 407265, 7 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273291

Digital Object Identifier
doi:10.1155/2014/407265

Mathematical Reviews number (MathSciNet)
MR3193512

Zentralblatt MATH identifier
07022330

Citation

Liu, Aibo; Liu, Changchun. Weak Solutions for a Sixth Order Cahn-Hilliard Type Equation with Degenerate Mobility. Abstr. Appl. Anal. 2014 (2014), Article ID 407265, 7 pages. doi:10.1155/2014/407265. https://projecteuclid.org/euclid.aaa/1412273291


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References

  • G. Gompper and J. Goos, “Fluctuating interfaces in microemulsion and sponge phases,” Physical Review E, vol. 50, no. 2, pp. 1325–1335, 1994.
  • I. Pawłow and W. M. Zaj\kaczkowski, “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.
  • Z. Wang and C. Liu, “Some properties of solutions for the sixth-order Cahn-Hilliard-type equation,” Abstract and Applied Analysis, vol. 2012, Article ID 414590, 24 pages, 2012.
  • C. Liu and Z. Wang, “Optimal control for a sixth order nonlinear parabolic equation,” Mathematical Methods in the Applied Sciences, 2013.
  • G. Schimperna and I. Pawłow, “On a class of Cahn-Hilliard models with nonlinear diffusion,” SIAM Journal on Mathematical Analysis, vol. 45, no. 1, pp. 31–63, 2013.
  • C. Liu, “Regularity of solutions for a sixth order nonlinear parabolic equation in two space dimensions,” Annales Polonici Mathematici, vol. 107, no. 3, pp. 271–291, 2013.
  • J. Simon, “Compact sets in the space ${L}^{p}(0,T;B)$,” Annali di Matematica Pura ed Applicata. Serie Quarta, vol. 146, pp. 65–96, 1987.
  • J. L. Lions, Quelques méthodes de résolution des problèmes aux limites nonlinéaires, Dunod, Paris, France, 1969. \endinput