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Asymptotic Attractors of Benjamin-Bona-Mahony Equations

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2008

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
In this paper, we consider the long time behavior of solution for the Benjamin-Bona-Mahony equations with periodic boundary conditions. By the method of orthogonal decomposition, we show that the existence of asymptotic attractor which overcome difficulty come from the precision of approximate inertial manifolds. Moreover, the dimensions estimate of the asymptotic attractor is obtained.
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  • English

REFERENCES

References: 

[1] J. Albert, Dispersion of low-energy waves for the generalized Benjamin-Bona-Mahony equation,
J. Diff. Equ., 63(1):117-134, 1986.
[2] J. Avrin, The generalized Benjamin-Bona-Mahony equation in Rn with singular initial data, Nonlin.
Anal., 11(1): 139-147, 1987.
[3] T. B. Benjamin, J. L. Bona and J. J. Mahony, Model equations for long waves in nonlinear dispersive
systems, Philos. Trans. Roy. Soc. Londan , 272(1): 47-78, 1972.
[4] P. Biler, Long time behaviour of solutions of the generalized Benjamin-Bona-Mahony equation in
two-space dimensions, Diff. Integ. Equ., 5(4): 891-901, 1992.
[5] A. O. Celebi, V. K. Kalantarov and M. Polat, Attractors for the generalized Benjamin-Bona-Mahony
equation, J. Diff. Equ., 157(2): 439-451, 1999.
[6] S. N. Chow and K. Lu, Inertial manifolds for flows in Banach spaces, J. Diff. Eqns., 74(1): 285-
317, 1988.
[7] C. Foias, O. Manley and R. Temam, Sur l’interaction des petits et grands tourbillons dans les
ecoulements turbulents, C. R. Acad. Sci. Paris, Serie I, 305: 497-500, 1987.
[8] C. Foias, G. Sell and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. Diff.
Eqns., 73(2): 309-353, 1988.
[9] M. Stanislavova, On the global attractor for the damped Benjamin-Bona-Mahony equation, Proceedings
of the fifth international conference on dynamical systems and differential equations, June
16-19, 2004, Pomona, CA, USA
[10] M. Stanislavova, A. Stefanov and B. Wang, Asymptotic Smoothing and attractors for the generalized
Benjamin-Bona-Mahony equation on R3, J. Diff. Equ., 219(2): 451-483, 2005.
[11] B. Wang, Strong Attracrors for the Benjamin-Bona-Mahony equation, Appl. Math. Lett., 10(1):
23-28, 1997.
[12] G. X. Wang, Z. R. Liu, The asymptotic attractors of Kuramoto-Sivashinsky equation, Acta Math.
Appl. Sinica(in Chinese), 23(2): 329-336, 2000.
[13] B. Wang, W. Yang, Finite dimensional behaviour for the Benjamin-Bona-Mahony equation, J.
Phys. A, Math. Gen., 30(12):4877-4885, 1997.
[14] C. S. Zhu, Global attractor for the damped Benjamin-Bona-Mahony equations on R1, Appl. Anal.,
86(1):59-65, 2007.
[15] C. S. Zhu, C. L. Mu, Exponential decay estimates for time-delayed Benjamin-Bona-Mahony equations,
Appl. Anal., 87(4):401-07, 2008.

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