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Volume 24 Issue 5
May  1998
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Journal of Beijing University of Aeronautics and Astronautics  > 1998  >  24(5): 584-587.
Liu Shenquan, Lu Qishao, Wang Qiet al. Traveling Waves of the Cahn-Hilliard Equation[J]. Journal of Beijing University of Aeronautics and Astronautics, 1998, 24(5): 584-587. (in Chinese)
Citation: Liu Shenquan, Lu Qishao, Wang Qiet al. Traveling Waves of the Cahn-Hilliard Equation[J]. Journal of Beijing University of Aeronautics and Astronautics, 1998, 24(5): 584-587. (in Chinese)
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Traveling Waves of the Cahn-Hilliard Equation

  • Beijing University of Aeronautics and Astronautics,Dept. of Applied Mathematics and Physics

  • Received Date: 12 Mar 1997
  • Publish Date: 31 May 1998
    Abstract
  • The asymptotic perturbation method is used to deal with the Cahn-Hilliard equation and obtain the inner and outer solutions of traveling waves. The two solutions are matched into one solution of the equation. The feature of the method not only matches the inner and outer solutions of the higher order partial differential equation, but also satisfies the boundary condition and initial condition. After a long time evolution, the solutions of the Cahn-Hillard equation have the structures of traveling waves as the limit states. The result in this paper can explain the theoretic and numerical simulation results of the Cahn-Hillard equation. The property of model fits well with that of the equation.

     

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  • 1. Cahn J W,Hilliard J E.Free energy of a nonuniform system(Ⅰ).J Chem Phys,1958,28:258~267 2. Alikakos N,Bates P W.Slow motion for the Cahn-Hilliard equation in one space dimension.J　Differential Equations,1991,90:81~135 3. Pego R L.Front migration in the nonlinear Cahn-Hilliard equation.Proc Roy Soc London Ses A,1989,422:261~278 4. Bates P W,Fife P C.The dynamics of nucleation for the Cahn-Hilliard equation.SIAM J Appl Math,1993,53(4):990~1008 5. Carr J,Gurtin M E,Slemrod M.Structured phase transitions on finite interval.Arch Rational Mech Anal,1984,86:317~351 6. Elliott C M,French D A.Numerical studies of the Cahn-Hilliard equation for phase separation.IMA J Appl Math,1987,38:97~128 7. Bates P W,Fife P C.Spectral comparison principles for the Cahn-Hilliard and phase-field equations and times scales for coarsening.Phys D,1990,43:335~348
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