SHANG Ya-dong, GUO Bo-ling. Exponential Attractor for the Generalized Symmetric Regularized Long Wave Equation With Damping Term[J]. Applied Mathematics and Mechanics, 2005, 26(3): 259-266.
Citation: SHANG Ya-dong, GUO Bo-ling. Exponential Attractor for the Generalized Symmetric Regularized Long Wave Equation With Damping Term[J]. Applied Mathematics and Mechanics, 2005, 26(3): 259-266.

Exponential Attractor for the Generalized Symmetric Regularized Long Wave Equation With Damping Term

  • Received Date: 2003-09-22
  • Rev Recd Date: 2004-11-27
  • Publish Date: 2005-03-15
  • The global fast dynamics for the generalized symmetric regularized long wave equation with damping term is considered. The squeezing property of the nonlinear semi-group associated with this equation and the existence of exponential attractor are proved. The upper bounds of its fractal dimension are also estimated.
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  • [1]
    Seyler E C,Fanstermacler D C.A symmetric regularized long wave equation[J].Phys Fluids,1984,27(1):4—7. doi: 10.1063/1.864487
    [2]
    Albert J. On the decay of solutions of the generalized BBM equation[J]. Journal of Mathematical Analysis and Applications,1989,141(2):527—537. doi: 10.1016/0022-247X(89)90195-9
    [3]
    Amick C J,Bona J L,Schonbek M E. Decay of solutions of some nonlinear wave equations[J].Journal of Differential Equations,1989,81(1):1—49. doi: 10.1016/0022-0396(89)90176-9
    [4]
    Ogino T,Takeda S. Computer simulation and analysis for the spherical and cylindrical Ion-acoustic solitons[J].Journal of Physics Society of Japan,1976,41(1): 257—264. doi: 10.1143/JPSJ.41.257
    [5]
    Makhankov V G. Dynamics of classical solitons (in non-integrable systems)[J].Physics Reports,A review section of physics letters (section C),1978,35C(1):1—128.
    [6]
    Clarkson P A. New similarity reductions and Painleve analysis for the symmetric regularized long wave and modified Benjamin-Bona-Mahoney equations[J].J Phys A: Math Gen,1989,22(18):3821—3848. doi: 10.1088/0305-4470/22/18/020
    [7]
    Bogolubsky J L. Some examples of inelastic soliton interaction[J].Computer Physics Communications,1977,13(1):149—155. doi: 10.1016/0010-4655(77)90009-1
    [8]
    CHEN Lin.Stability and instability of solitary wave for generalized symmetric regularized long wave equations[J].Physica D,1998,118(1/2):53—68. doi: 10.1016/S0167-2789(97)00325-4
    [9]
    GUO Bo-ling.The spectral method for symmetric regularized wave equations[J].Journal of Computational Mathematics,1987,5(4):297—306.
    [10]
    MIAO Chen-xia.The initial boundary value problem for symmetric long wave equations with non-homogeneous boundary value[J].Northeastern Mathematics Journal,1994,10(4):463—472.
    [11]
    SHANG Ya-dong,GUO Bo-ling,FANG Shao-mei.Long time behavior of the dissipative generalized symmetric regularized long wave equations[J].Journal of Partial Differential Equations,2002,15(1):21—35.
    [12]
    SHANG Ya-dong,GUO Bo-ling. Finite dimensional behavior for the dissipative generalized symmetric regularized long wave equations[J].Journal of Systems Science and Complexity,2003,16(2):236—248.
    [13]
    Babin A V,Vishik M I.Regular attractors of semigroup and evolution equations[J].Journal of Mathematics Pure and Applications,1983,62(5):441—491.
    [14]
    Eden A,Foias C,Nicolaenko B,et al.Exponential Attractors for Dissipative Evolution Equations[M].New York:Masson,Paris,Wiely,1994,36—48.
    [15]
    戴正德,郭柏灵.惯性流形和近似惯性流形[M].北京:科学出版社,2000,226—242.
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