Advertisement

Applied Mathematics and Mechanics

, Volume 16, Issue 1, pp 37–45 | Cite as

The inertial fractal set for weakly damped forced korteweg-de-vries equation

  • Dai Zheng-de
  • Zhu Zhi-wei
Article

Abstract

In this paper we consider weakly damped forced Korteweg-de-Vries equation with non-self-adjoint operator. The existence of inertial fractal set M of this equation is proved, the estimates of the upper bounds of fractal dimension for M are also obtained.

Key words

KdV equation inertial fractal dimension 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ghidaglia, J. M., Weakly damped forced Korteweg-de-Vries equations behave as a finite dimensional dynamical system in the long time.J. Diff. Equ.,74, 2 (1988), 369–390.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Constantin, P., C. Foias and R. Temam, Attractors representing turbulent Flows,Mem. Amer. Math. Soc., 314 (1985), 53.MathSciNetGoogle Scholar
  3. [3]
    Constantin, P., C. Foias, B. Nicolaenko and R. Temam,Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, Springer-Verlag (1989).Google Scholar
  4. [4]
    Eden, A., C. Foias, B. Nicolaenko and R. Temam, Inertial sets for dissipative evolution eguations,IMA. Preprint. Series, 812 (1991).Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1995

Authors and Affiliations

  • Dai Zheng-de
    • 1
    • 2
  • Zhu Zhi-wei
    • 3
  1. 1.Institute of Applied MathematicsYunnan Province
  2. 2.Department of Math.Yumnan Univ.KunmingChina
  3. 3.Department of Math.Xijang UniversityXifangChina

Personalised recommendations