\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures

Abstract Related Papers Cited by
  • An initial-boundary-value problem for the sixth order Cahn-Hilliard type equation in 3-D is studied. The problem describes phase transition dynamics in ternary oil-water-surfactant systems. It is based on the Landau-Ginzburg theory proposed for such systems by G. Gompper et al. We prove that the problem under consideration is well posed in the sense that it admits a unique global smooth solution which depends continuously on the initial datum.
    Mathematics Subject Classification: Primary: 35K50, 35K60; Secondary: 35Q72, 35L205.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    J. Berry, K. R. Elder and M. Grant, Simulation of an atomistic dynamic field theory for monatomic liquids: Freezing and glass formation, Phys. Rev. E, 77 (2008), 061506.

    [2]

    J. Berry, M. Grant and K. R. Elder, Diffusive atomistic dynamics of edge dislocations in two dimensions, Phys. Rev. E, 73 (2006), 031609.

    [3]

    O. V. Besov, V. P. Il'in and S. M. Nikolskij, "Integral Representation of Functions and Theorems of Imbeddings," Nauka, Moscow, 1975 (in Russian).

    [4]

    C. M. Dafermos and L. Hsiao, Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity, Nonlinear Anal., 6 (1982), 435-454.

    [5]

    K. R. Elder and M. Grant, Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals, Phys. Rev. E, 70 (2004), 051605.

    [6]

    P. Galenko, D. Danilov and V. Lebedev, Phase-field-crystal and Swift-Hohenberg equations with fast dynamics, Phys. Rev. E, 79 (2009), 051110(11).

    [7]

    G. Gompper and J. Goos, Fluctuating interfaces in microemulsion and sponge phases, Phys. Rev. E, 50 (1994), 1325-1335.

    [8]

    G. Gompper and M. Kraus, Ginzburg-Landau theory of ternary amphiphilic systems. I. Gaussian interface fluctuations, Phys. Rev. E, 47 (1993), 4289-4300.

    [9]

    G. Gompper and M. Kraus, Ginzburg-Landau theory of ternary amphiphilic systems. II. Monte Carlo simulations, Phys. Rev. E, 47 (1993), 4301-4312.

    [10]

    G. Gompper and M. Schick, Correlation between structural and interfacial properties of amphiphilic systems, Phys. Rev. Lett., 65 (1990), 1116-1119.

    [11]

    G. Gompper and M. Schick, Self-assembling amphiphilic system, in "Phase Transitions and Critical Phenomena" (C. Domb and J. Lebowitz eds.), vol. 16, pages 1-176, London, 1994, Academic Press.

    [12]

    G. Gompper and S. Zschocke, Ginzburg-Landau theory of oil-water-sur-factant mixtures, Phys. Rev. A, 46 (1992), 4836-4851.

    [13]

    M. D. Korzec, P. L. Evans, A. Münch and B. Wagner, Stationary solutions of driven fourth-and sixth-order Cahn-Hilliard type equations, SIAM J. Appl. Math., 69 (2008), 348-374.

    [14]

    M. Korzec, P. Nayar and P. Rybka, Global weak solutions to a sixth order Cahn-Hilliard type equation, (2011), to appear.

    [15]

    J.-L. Lions and E. Magenes, "Nonhomogeneous Boundary Value Problems and Applications," Vol. I, II, Springer Verlag, New York, 1972.

    [16]

    T. V. Savina, A. A. Golovin, S. H. Davis, A. A. Nepomnyashchy and P. W. Voorhees, Faceting of a growing crystal surface by surface diffusion, Phys. Rev. E, 67 (2003), 021606.

    [17]

    V. A. Solonnikov, A priori estimates for solutions of second order parabolic equations, Trudy Mat. Inst. Steklov, 70 (1964), 133-212 (in Russian).

    [18]

    V. A. Solonnikov, Boundary value problems for linear parabolic systems of differential equations of general type, Trudy Mat. Inst. Ste-klov, 83 (1965), 1-162 (in Russian).

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(123) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return