ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS

doi:10.1016/S0252-9602(12)60190-8

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (6): 2431-2452.doi: 10.1016/S0252-9602(12)60190-8

• 论文 • 上一篇

ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS

张法勇¹|郭柏灵²

1.Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China；School of Mathematical Science, Heilongjiang University, Harbin 150080, China； 2.Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

收稿日期:2010-09-17 出版日期:2012-11-20 发布日期:2012-11-20
基金资助:
The research was Supported by the National Natural Science Foundation of China (10371077).

ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS

ZHANG Fa-Yong¹, GUO Bai-Ling²

1.Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China；School of Mathematical Science, Heilongjiang University, Harbin 150080, China； 2.Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2010-09-17 Online:2012-11-20 Published:2012-11-20
Supported by:
The research was Supported by the National Natural Science Foundation of China (10371077).

摘要/Abstract

摘要：

A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L² ×H¹ ×H² over a finite time interval (0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

关键词: dissipative Zakharov equations, dynamical system, global attractor, finite difference method

Abstract:

Key words: dissipative Zakharov equations, dynamical system, global attractor, finite difference method

中图分类号:

65M06

张法勇, 郭柏灵. ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS[J]. 数学物理学报(英文版), 2012, 32(6): 2431-2452.

ZHANG Fa-Yong, GUO Bai-Ling. ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS[J]. Acta mathematica scientia,Series B, 2012, 32(6): 2431-2452.

参考文献

[1] Babin A V, Vishik M I. Regular attractors of semigroups and evolution equations. J Math Pures Appl, 1983, 62: 441–491

[2] Babin A V, Vishik M I. Attractors of Evolution Equations. Moscow: Nauka, 1989; English Translation, North-Holland, 1992

[3] Hale J K. Asymptotic Behavior of Dissipative Systems. AMS Mathematical Surveys and Monographs 25. Providence, RI: Amer Math Soc, 1988

[4] Glassey R T. Convergence of an energy-preserving scheme for the Zakharov equations in one space dimension. Math Comp, 1992, 58: 83–102

[5] Glassey R T. Approximate solutions to the Zakharov equations via finite differences. J Comput Phys, 1992, 100: 377–383

[6] Chang Q S, Guo B L, Jiang H. Finite difference method for generalized Zakharov equations. Math Comp, 1995, 64: 537–553

[7] Chang Q S, Guo B L. Attractors and dimensions for discretizations of a dissipative Zakharov equations. Acta Math Appl Sinica, 2002, 18: 201–214

[8] Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. 2nd ed. New York: Springer-Verlag, 1997

[9] Flahaut I. Attractors for the dissipative Zakharov system. Nonlinear Analysis, TMA, 1991, 16: 599–633

[10] Zakharov V E. Collapse of Langmuir waves. Soviet Phys JETP, 1972, 35: 908–912

[11] Sulem C, Sulem P L. Regularity properties for the equations of Langmuir turbulence. C R Acad Sci Paris Ser A Math, 1979, 289: 173–176

[12] Guo B L, Shen L J. The existence and uniqueness of classical solution to the periodic initial value problem for Zakharov equations. Acta Math Appl Sinica, 1982, 5: 310–324

[13] Yan Yin. Attractors and dimensions for discretizations of a weakly damped Schr¨odinger equation and a Sine–Gorden equation. Nonlinear Analysis, TMA, 1993, 20: 1417-1452

[14] Zhang F Y. Long-time behavior of finite difference solutions of three-dimensional nonlinear Schr¨odinger equation with weakly damped. J Comput Math, 2004, 22: 593–604

[15] Zhang F Y. The finite difference method for dissipative Klein–Gordon–Schr¨odinger equations in three space dimensions. J Comput Math, 2010, 28: 879–900

ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS

ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	Azer KHANMAMEDOV, Sema YAYLA. LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R^N[J]. 数学物理学报(英文版), 2018, 38(3): 1025-1042.
[2]	张磊, 刘斌. THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM[J]. 数学物理学报(英文版), 2018, 38(2): 651-672.
[3]	武利猛, 张娟, 倪明康, 陆海波. ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS[J]. 数学物理学报(英文版), 2016, 36(5): 1457-1466.
[4]	赵文强. REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE[J]. 数学物理学报(英文版), 2016, 36(2): 409-427.
[5]	李名田, 马际华. ON A LEMMA OF BOWEN[J]. 数学物理学报(英文版), 2014, 34(3): 932-940.
[6]	汪永海, 王灵芝. TRAJECTORY ATTRACTORS FOR NONCLASSICAL DIFFUSION EQUATIONS WITH FADING MEMORY[J]. 数学物理学报(英文版), 2013, 33(3): 721-737.
[7]	陈慧琴, 段金桥, 张诚坚. ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LÉVY NOISES[J]. 数学物理学报(英文版), 2012, 32(4): 1391-1398.
[8]	陈学勇, 刘伟安. GLOBAL ATTRACTOR FOR A DENSITY-DEPENDENT SENSITIVITY CHEMOTAXIS MODEL[J]. 数学物理学报(英文版), 2012, 32(4): 1365-1375.
[9]	Alain Haraux, Mohamed Ali Jendoubi. ON A SECOND ORDER DISSIPATIVE ODE IN HILBERT SPACE WITH AN INTEGRABLE SOURCE TERM[J]. 数学物理学报(英文版), 2012, 32(1): 155-163.
[10]	Alen Alexanderian, Muruhan Rathinam, Rouben Rostamian. HOMOGENIZATION, SYMMETRY, AND PERIODIZATION IN DIFFUSIVE RANDOM MEDIA[J]. 数学物理学报(英文版), 2012, 32(1): 129-154.
[11]	袁益让. THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM[J]. 数学物理学报(英文版), 2011, 31(3): 857-881.
[12]	H. Kim, M. Laforest, D. Yoon. AN ADAPTIVE VERSION OF GLIMM'S SCHEME[J]. 数学物理学报(英文版), 2010, 30(2): 428-446.
[13]	张引娣, 李开泰. EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE H^k[J]. 数学物理学报(英文版), 2009, 29(5): 1165-1172.
[14]	应隆安. THE ASYMPTOTIC LIMIT FOR A COMBUSTION MODEL IN REGARD TO INFINITE REACTION RATE[J]. 数学物理学报(英文版), 2008, 28(4): 924-932.
[15]	黎育红; Zdzislaw Brzezniak; 周建中. CONCEPTUAL ANALYSIS AND RANDOM ATTRACTOR FOR DISSIPATIVE RANDOM DYNAMICAL SYSTEMS[J]. 数学物理学报(英文版), 2008, 28(2): 253-268.