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

Initial boundary value problem for the singularly perturbed Boussinesq-type equation

Abstract Related Papers Cited by
  • We are concerned with the singularly perturbed Boussinesq-type equation including the singularly perturbed sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number (surface tension parameter) less than but very close to $1/3$. The existence and uniqueness of the global generalized solution and the global classical solution of the initial boundary value problem for the singularly perturbed Boussinesq-type equation are proved.
    Mathematics Subject Classification: Primary: 35A01, 35L35; Secondary: 35G31, 35Q35.

    Citation:

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

    R. A. Admas, "Sobolev Space", Academic Press, New York, 1975.

    [2]

    P. Darapi and W. Hua, A numerical method for solving an ill-posed Boussinesq equation arising in water waves and nonlinear lattices, Appl. Math. Comput., 101 (1999), 159-207.

    [3]

    P. Darapi and W. Hua, Weakly non-local solitary wave solutions of a singularly perturbed Boussinesq equation, Math. Comput. Sim., 55 (2001), 393-405.

    [4]

    R. K. Dash and P. Darapi, Analytical and numerical studies of a singularly perturbed Boussinesq equation, Appl. Math. Comput., 126 (2002), 1-30.

    [5]

    Z. S. Feng, Traveling solitary wave solutions to the generalized Boussinesq equation, Wave Motion, 37 (2003), 17-23.

    [6]

    A. Friedman, "Partial Differential Equation of Parabolic Type", Prentice Hall, Eagliweed Cliffs, NJ, 1964.

    [7]

    H. A. Levine and B. D. Sleeman, A note on the non-existence of global solutions of initial boundary value problems for the Boussinesq equation $u_{t t} = 3u_{x x x x} + u_{x x} - 12(u^2)_{x x}$, J. Math. Anal. Appl., 107 (1985), 206-210.

    [8]

    Z.J. Yang, On local existence of solutions of initial boundary value problems for the "bad'' Boussinesq-type equation, Nonlinear Anal. TMA, 51 (2002), 1259-1271.

    [9]

    Y. L. Zhou and H. Y. Fu, Nonlinear hyperbolic systems of higher order generalized Sine-Gordon type, Acta Math. Sinica, 26 (1983), 234-249.

  • 加载中
Open Access Under a Creative Commons license
SHARE

Article Metrics

HTML views() PDF downloads(71) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return