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耗散的量子Zakharov方程解的渐进性行为

郭艳凤 郭柏灵 李栋龙

郭艳凤, 郭柏灵, 李栋龙. 耗散的量子Zakharov方程解的渐进性行为[J]. 应用数学和力学, 2012, 33(4): 486-499. doi: 10.3879/j.issn.1000-0887.2012.04.009
引用本文: 郭艳凤, 郭柏灵, 李栋龙. 耗散的量子Zakharov方程解的渐进性行为[J]. 应用数学和力学, 2012, 33(4): 486-499. doi: 10.3879/j.issn.1000-0887.2012.04.009
GUO Yan-feng, GUO Bo-ling, LI Dong-long. Asymptotic Behaviors of the Solutions for Dissipative Quantum Zakharov Equations[J]. Applied Mathematics and Mechanics, 2012, 33(4): 486-499. doi: 10.3879/j.issn.1000-0887.2012.04.009
Citation: GUO Yan-feng, GUO Bo-ling, LI Dong-long. Asymptotic Behaviors of the Solutions for Dissipative Quantum Zakharov Equations[J]. Applied Mathematics and Mechanics, 2012, 33(4): 486-499. doi: 10.3879/j.issn.1000-0887.2012.04.009

耗散的量子Zakharov方程解的渐进性行为

doi: 10.3879/j.issn.1000-0887.2012.04.009
基金项目: 国家自然科学基金资助项目(11061003)
详细信息
    通讯作者:

    郭艳凤(1976—),女,河南新乡人,副教授,博士(联系人.Tel: +86-772-2687015-802; E-mail: guoyan-feng@yahoo.com.cn).

  • 中图分类号: O175.2

Asymptotic Behaviors of the Solutions for Dissipative Quantum Zakharov Equations

  • 摘要: 主要研究量子Zakharov方程.在先验估计的基础上通过标准的Galerkin逼近方法得到了量子Zakharov方程解的存在唯一性.同时,也讨论了相应的解的渐进性行为,并且构造出在不同的能量空间上弱拓扑意义下的全局吸引子.
  • [1] Markowich P A, Ringhofer C A, Schmeiser C. Semiconductor Equations[M]. Vienna: Springer, 1990.
    [2] Jung Y D. Quantum-mechanical effects on electron-electron scattering in dense high-temperature plasmas[J]. Phys Plasmas, 2001, 8(8): 3842-3844.
    [3] Kremp D, Bornath Th, Bonitz M, Schlanges M. Quantum kinetic theory of plasmas in strong laser fields[J]. Phys Rev E, 1999, 60(4): 4725-4732.
    [4] Manfredi G, Haas F. Self-consistent fluid model for a quantum electron gas[J]. Phys Rev B, 2001, 64(7): 075316.
    [5] Haas F, Garcia L G, Goedert J, Manfredi G. Quantum ion-acoustic waves[J]. Phys Plasmas, 2003, 10(10): 3858-3866.
    [6] López J L. Nonlinear Ginzburg-Landau-type approach to quantum dissipation[J].Phys Rev E, 2004, 69(2): 026110.
    [7] Garcia L G, Haas F, de Oliveira L P L, Goedert J. Modified Zakharov equations for plasmas with a quautum correction[J]. Phys Plasmas, 2005, 12(1): 012302-8.
    [8] Zakharov V E. Collapse of Langmuir waves[J]. Sov Phys JETP, 1972, 35: 908-914.
    [9] Flahaut I. Attactors for the dissipative Zakharov system[J]. Nonlinear Analysis, TMA, 1991, 16(7/8): 599-633.
    [10] Guo B, Shen L. The global existence and uniqueness of classical solutions of periodic initial boundary problems of Zakharov equations[J]. Acta Math Appl Sin, 1982, 5(2): 310-324.
    [11] Guo B. On the IBVP for some more extensive Zakharov equations[J]. J Math Phys, 1987, 7(3): 269-275.
    [12] Goubet O, Moise I. Attractors for dissipative Zakharov system[J]. Nonlinear Analysis, TMA, 1998, 31(7): 823-847.
    [13] Li Y. On the initial boundary value problems for two dimensional systems of Zakharov equations and of complex-Schrdinger-real-Boussinesq equations[J]. J P Diff Eq, 1992, 5(2): 81-93.
    [14] Bourgain J. On the Cauchy and invariant measure problem for the periodic Zakharov system[J]. Duke Math J, 1994, 76(1): 175-202.
    [15] Bourgain J, Colliander J. On wellposedness of the Zakharov system[J]. Internat Math Res Notices, 1996, 11: 515-546.
    [16] Bejenaru I, Herr S, Holmer J, Tataru D. On the 2D Zakharov system with L2 Schrdinger data[J]. Nonlinearity, 2009, 22(5): 1063-1089.
    [17] Chueshov I D, Shcherbina A S. On 2D Zakharov system in a bounded domain[J]. Diff Int Eq, 2005, 18(7): 781-812.
    [18] Ghidaglia J M, Temam R. Attractors for damped nonlinear hyperbolic equations[J]. J Math Pure Appl, 1987, 66(3): 273-319.
    [19] Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics[M]. New York: Springer-Verlag, 1988.
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出版历程
  • 收稿日期:  2011-05-09
  • 修回日期:  2012-02-02
  • 刊出日期:  2012-04-15

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