Local Attractors for the Weakly Damped Forced KdV Equation in Thin 2D Domains
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Abstract: The existence of local attractors in thin 2D domains for the weakly damped forced KdV equation, whose principal operator is a non-self adjoint and non-sectorial one is given.
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[1] Temam R,Wang S.Inertial forms of Navier-Stokes equations on the sphere[J].J Funct Anal,1993,117(2):215-242. [2] Eden A,Foias C,Nicolaenko B,et al.Exponential attractors and their relevance to fluid dynamics systems[J].Phys D,1993,63(4):350-360. [3] Debussche A,Dubois T.Approximation of exponential order of the attractor of turbulent flow[J].Phys D,1994,72(4):372-389. [4] Sell G R.Global attractors for the three-dimensional Navier-Stokes equations[J].J Dynamics Differential Equations,1996,8(1):1-37. [5] Robinsion J C.Some closure results for inertial manifold[J].J Dynamics Differential Equations,1997,9(3):373-400. [6] LIU Zeng-rong,XU Zhen-yuan.A new method of studying the dy namical behaviour of the sine-Gordon equation[J].Phys Lett A,1995,20 4(5):343-346. [7] Eden A,Milani A,Nicolaenko B.Local exponetical attractor's for modes of phase change for compressible gas dynamics[J].Nonlinearity,1993,6(1):93-117. [8] Hale J K.Asymptotic Behaviour of Dissipative Systems[M].AMS Math Surv Monogr.New York:Springer-Verlag,1988. [9] Sell G,Taboada M.Local dissipativity and attractors for the K-S equation in thin 2D domains[J].Nonlinear Anal,1992,18(7):671-687. [10] Babin A V.Inertial manifolds for travelling wave solutions of reaction diffusion systems[J].Comm Pure Appl Math,1995,18(1):167-198. [11] Ghidaglia J M.Weakly damped forced Korteweg-de Vries equations be have as a finite dimensional dynamical system in the long time[J].J Differ ential Equations,1988,74(2):369-390. [12] Ghidaglia J M.A note on the strong convergence towards attractors of damped forced KdV equations[J].J Differential Equations,1994,110(2):356-359. [13] 田立新,徐振源.弱阻尼KdV方程中长期动力学行为研究[J].应用数学和 力学,1997,18(10):953-958. [14] 谷超豪.孤立子理论及应用[M].应用数学丛书.杭州:浙江大学出版社,1990. [15] 郭柏灵.非线性演化方程[M].非线性科学丛书.上海:上海科技教育出版社,1995. [16] 田立新,刘玉荣,刘曾荣.窄域上2D弱阻尼KdV方程的blow-up的研究[J].应用数学和力学,2000,21(10):1002-1008. [17] Balmforth N L,Ierley G R,Worthing R.Pulse dynamics in unstable medium[J].SIAM J Appl Math,1997,57(1):205-251.
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