Asymptotic Behaviors of the Solutions for Dissipative Quantum Zakharov Equations

GUO Yan-feng; GUO Bo-ling; LI Dong-long

doi:10.3879/j.issn.1000-0887.2012.04.009

Volume 33 Issue 4

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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

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Asymptotic Behaviors of the Solutions for Dissipative Quantum Zakharov Equations

doi: 10.3879/j.issn.1000-0887.2012.04.009

¹Department of Information and Computation of Science, Guangxi University of Technology, Guangxi Liuzhou 545006, P.R.China;²Institute of Applied Physics and Computational Mathematics,Beijing 100088, P.R.China

Received Date: 2011-05-09
Rev Recd Date: 2012-02-02
Publish Date: 2012-04-15

Abstract

Abstract

The dissipative quantum Zakharov equations were mainly studied. The existence and uniqueness of the solutions for dissipative quantum Zakharov equations were proved by the standard Galerkin approximation method on the basis of a priori estimates. Meanwhile, the asymptotic behavior of solutions and the global attractor which was constructed in energy space equipped with weak topology were also investigated.
- quantum Zakharov equations,
- absorbing set,
- global attractor

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References(19)

References

[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.