Global Attractor of Two-Dimensional Strong Damping KDV Equation and Its Dimension Estimation
ABSTRACT
Firstly, a priori estimates are obtained for the existence and uniqueness of solutions of two dimensional KDV equations, and prove the existence of the global attractor, finally get the upper bound estimation of the Hausdorff and fractal dimension of attractors.
Cite this paper
C. Zhang and G. Lin, "Global Attractor of Two-Dimensional Strong Damping KDV Equation and Its Dimension Estimation," Applied Mathematics, Vol. 5 No. 1, 2014, pp. 7-15. doi: 10.4236/am.2014.51002.
C. Zhang and G. Lin, "Global Attractor of Two-Dimensional Strong Damping KDV Equation and Its Dimension Estimation," Applied Mathematics, Vol. 5 No. 1, 2014, pp. 7-15. doi: 10.4236/am.2014.51002.
References
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[1] G. R. Sell, “Global Attractors for the Three-Dimensional Navier-Stokes Equations,” Journal of Dynamics and Di_erential Equations, Vol. 1, 1996. [2] J. K. Hale, “Asymptotic Behaviour of Dissipative Systems,” Mathematical Surveys and Monographs, Vol. 25, 1988. [3] G. Sell and M. Taboada, “Local Dissipativity and Attractors for the K-S Equation in Thin 2D Domains,” Journal of Non-linear Analysis, Vol. 7, 1992. [4] R. Temam and S. Wang, “Inertial Forms of Navier-Stokes Equations on the Sphere,” Journal of Functional Analysis, Vol. 2, 1993. [5] B. L. Guo and Y. S. Li, “Attractor for Dissipative Klein-Gordon-Schrdinger Equations in R3,” Journal of Differential Equations, Vol. 2, 1997. [6] X. Y. Du and Z. D. Dai, “Global Attractor of Dissipative KDV Equation about Cauchy Problem,” Acta Mathematica Scientia, Vol. 20, 2000. [7] L. X. Tian, Y. R. Liu and Z. R. Liu, “The Narrow 2D Weak Local Attractor for Damped KDV Equation,” Applied Mathematics and Mechanics, Vol. 21, 2000. [8] B. L. Guo, “Method of Vanishing Viscosity and Viscosity Difference Format,” Science Press, Beijing, 1993. [9] G. G. Lin, “Nonlinear Evolution Equation,” Yunnan University Press, Yunnan, 2011.