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Applicable Analysis
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Articles

On the regularity of the global attractor for a damped Rosenau equation on R

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Pages 1285-1294 | Received 16 Dec 2015, Accepted 06 May 2016, Published online: 25 May 2016

References

  • Rosenau P. A quasi-continuous description of a nonlinear transmission line. Phys. Scripta. 1986;34:827–829.
  • Rosenau P. Dynamics of dense discrete systems-high order effects-. Progr. Theor. Phy. 1988;79:1028–1042.
  • Benjamin TB, Bona JL, Mahony JJ. Model equations for long waves in nonlinear dispersive systems. Philos. Trans. Roy. Soc. London. 1972;272:47–78.
  • Peregrine DH. Calculations of the development of an undular bore. J. Fluid Mech. 1966;25:321–330.
  • Avrin J, Goldstein JA. Global existence for the Benjamin--Bona--Mahony equation in arbitrary dimensions. Nonlinear Anal. 1985;9:861–865.
  • Avrin J. The generalized Benjamin--Bona--Mahony equation in R\textsuperscript{n} with singular initial data. Nonlinear Anal. 1987;11:139–147.
  • Avrin J. On the decay of solutions of the generalized Benjamin--Bona--Mahony equation. J. Math. Anal. Appl. 1989;141:527–537.
  • Bona JL, Tzvetkov N. Sharp well-posedness results for the BBM equation. Discrete Contin. Dyn. Syst. 2009;4:1241–1252.
  • Celebi AO, Polat VK. Attractors for the generalized Benjamin--Bona--Mahony equation. J. Differ. Equ. 1999;157:439–451.
  • Fang S, Guo B. The decay rates of solutions of generalized Benjamin--Bona--Mahony equations in multi-dimensions. Nonlinear Anal. 2008;69:2230–2235.
  • Fang S, Guo B. H\textsuperscript{m} convergence rates of solutions of GBBM equations in multi-dimensional spaces. Prog. Nat. Sci. 2009;19:1053–1057.
  • Guo Y, Wang M, Tang Y. Higher regularity of global attractor for a damped Benjamin--Bona--Mahony equation on ℝ. Appl. Anal. 2015;94:1766–1783.
  • Mei M. Lq-decay rates of solutions for Benjamin--Bona--Mahony--Burgers equations. J. Differ. Equ. 1999;158:314–340.
  • Park JY, Park SH. Pullback attractors for the non-autonomous Benjamin--Bona--Mahony equation in unbounded domains. Sci. China Math. 2011;54:741–752.
  • Stanislavova M. On the global attractor for the damped Benjamin--Bona--Mahony equation. In: Proceedings of the fifth international conference on dynamical systems and differential equations; 2004 Jun 16--19; Pomona (CA); 2004.
  • Stanislavova M, Stefanov A, Wang B. Asymptotic smoothing and attractors for the generalized Benjamin--Bona--Mahony equation on R\textsuperscript{3}. J. Differ. Equ. 2005;219:451–483.
  • Wang B. Strong attractors for the Benjamin--Bona--Mahony equation. Appl. Math. Lett. 1997;10:23–28.
  • Wang B. Regularity of attractors for the Benjamin--Bona--Mahony equation. J. Phys. A. 1998;31:7635–7645.
  • Wang B. Attractors and approximate inertial manifolds for the generalized Benjamin--Bona--Mahony equation. Math. Method Appl. Sci. 1997;20:189–203.
  • Wang B, Fussner DW, Bi C. Existence of global attractors for the Benjamin--Bona--Mahony equation in unbounded domains. J. Phys. A. 2007;40:10491–10504.
  • Wang B, Yang W. Finite-dimensional behaviour for the Benjamin--Bona--Mahony equation. J. Phys. A. 1997;30:4877–4885.
  • Wang M. Long time dynamics for a damped Benjamin--Bona--Mahony equation in low regularity spaces. Nonlinear Anal. 2014;105:134–144.
  • Zhu C. Global attractor for the damped Benjamin--Bona--Mahony equations on ℝ1. Appli Anal. 2007;86:59–65.
  • Zhu C. Asymptotic attractors of Benjamin--Bona--Mahony equations. Eur. J. Pure Appl. Math. 2008;1:3–10.
  • Zhu C, Mu C. Exponential decay estimates for time-delayed Benjamin--Bona--Mahony equations. Appl. Anal. 2008;87:401–407.
  • Esfahani A, Pourgholi R. Dynamics of solitary waves of the Rosenau-RLW equation. Differ. Equ. Dyn. Syst. 2014;22:93–111.
  • Liu L, Mei M, Wong YS. Asymptotic behavior of solutions to the Rosenau--Burgers equation with a periodic initial boundary. Nonlinear Anal. 2007;67:2527–2539.
  • Liu L, Mei M. A better asymptotic profile of Rosenau--Burgers equation. Appl. Math. Comput. 2002;131:147–170.
  • Mei M. Long-time behavior of solution for Rosenau--Burgers equation I. Appl. Anal. 1996;63:315–330.
  • Mei M. Long-time behavior of solution for Rosenau--Burgers equation II. Appl. Anal. 1998;68:333–356.
  • Park MA. On the Rosenau equation. Comput. Appl. Math. 1990;9:145–152.
  • Park MA. On nonlinear dispersive equations. Differ. Integr. Equ. 1996;9:1331–1335.
  • Zhou D, Mu C. Homogeneous initial-boundary value problem of the Rosenau equation posed on a finite interval. Appl. Math. Lett. 2016;57:7–12.
  • Wang M. Global attractor for weakly damped gKdV equations in higher Sobolev spaces. Discrete Contin. Dyn. Syst. 2015;35:3799–3825.
  • Miao CX, Wu JH, Zhang ZF. Littlewood-Paley theorem and its applications in fluid dynamics. Beijing: Science Press; 2011. Chinese.
  • Pazy A. Semigroups of linear operators and applications to partial differential equations. Applied mathematical sciences. Springer verlag; 1983.
  • Babin AV, Vishik MI. Attractors of evolution equations. Amsterdam: North-Holland; 1992.
  • Hale JK. Asymptotic behavior of dissipative systems. Vol. 25, Mathematical surveys and monographs. American Mathematical Society; 1988.
  • Temam R. Infinite-dimensional dynamical systems in mechanics and physics. Vol. 68, Applied mathematics. New York (NY): Springer-Verlag; 1988.
  • Reed M, Simon B. Methods of modern mathematical physics IV. Analysis of operator. New York (NY): Acadamic Press; 1978.
  • Evans LC. Partial differential equations. American Mathematical Society; 1998.

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