带可乘白噪音的非线性耦合复Ginzburg-Landau方程组的随机吸引子
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摘要
研究一类带可乘白噪音的非线性耦合复Ginzburg-Landau方程组的随机吸引子,采用解的先验估计和Ball创建的能量方程方法,证明了在初始条件和周期边界条件下它的随机吸引子的存在性。证明过程分成3个步骤:首先对方程组的可乘白噪音进行预处理,使得随机微分项消失;其次证明方程组对应的随机动力系统在H中和V中存在吸收集,最后得到Ginzburg-Landau方程组在H中存在随机吸引子。
In this paper,the random attractor of the nonlinear coupled complex Ginzburg-Landau equations with multiplicative white noise are investigated.Under the initial condition and periodic boundary condition,the existence of random attractors for the complex equations is proven using the prior estimate of solutions and the method of energy equations introduced by Ball.It could be divided into three steps:first,it preprocesses the multiplicative white noise terms,which makes the stochastic differential item disappear.And then,the existence of absorbing set of stochastic dynamical system associated with the nonlinear coupled complex Ginzburg-Landau equations in H and Vis proven.Finally,it proves the existence of random attractor when equations are in H.
In this paper,the random attractor of the nonlinear coupled complex Ginzburg-Landau equations with multiplicative white noise are investigated.Under the initial condition and periodic boundary condition,the existence of random attractors for the complex equations is proven using the prior estimate of solutions and the method of energy equations introduced by Ball.It could be divided into three steps:first,it preprocesses the multiplicative white noise terms,which makes the stochastic differential item disappear.And then,the existence of absorbing set of stochastic dynamical system associated with the nonlinear coupled complex Ginzburg-Landau equations in H and Vis proven.Finally,it proves the existence of random attractor when equations are in H.
引文
[1]蒋燕,刘建国.(3+1)维变系数Kadomtsev-Petviashvili方程的多孤子解[J].南昌大学学报(理科版),2014,38(6):527-529.
[2]金国华,曾志芳.(2+1)维变系数Nizhnik-Novikov-Veselov方程的孤子解[J].南昌大学学报(理科版),2015,39(3):229-231.
[3]万亮,龚雅玲,刘建国.广义Kuramoto-Sivashinsky方程的孤子解[J].南昌大学学报(理科版),2015,39(4):319-322.
[4]蒋燕.(2+1)维变系数Kadomtsev-Petviashvili方程新的精确解[J].南昌大学学报(理科版),2015,39(5):423-425.
[5]秦立春.广义双曲函数法求解(2+1)维变系数NizhnikNovikov-Veselov方程新的孤子解[J].南昌大学学报(理科版),2016,40(2):107-116.
[6]丁瑶.(2+1)维Potential Kadomtsev-Petviashvili方程新的精确解[J].南昌大学学报(理科版),2016,40(6):528-531.
[7]黄伟凡.(2+1)维破裂孤子方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(1):8-12.
[8]赵欢,邱震钰.(3+1)维破裂孤子方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(2):114-117.
[9]熊伟.(3+1)维Yu-Toda-Sasa-Fukuyama方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(3):211-215.
[10]袁娜.(3+1)维Boiti-Leon-Manna-Pempinelli方程新的三波解[J].南昌大学学报(理科版),2017,41(4):319-323.
[11]付中华,李良树.(G'/G)展开法求解(3+1)维JimboMiwa方程新的精确解[J].南昌大学学报(理科版),2017,41(5):418-422.
[12]秦立春.Caudrey-Dodd-Gibbon-Kaeada方程的新双周期孤子解[J].南昌大学学报(理科版),2017,41(6):524-526.
[13]莫春鹏,李栋龙.复Ginzburg-Landau方程整体解的存在性[J].广西工学院学报,2006,17(3):17-20.
[14]杨林,黄琼伟,戴正德.双核非线性光导纤维材料的整体吸引子[J].湖南大学学报(自然科学版),2009,25(3):12-16.
[15]王蕊,李扬荣.带有可乘白噪音的广义Ginzburg-Landau方程的随机吸引子[J].西南大学学报(自然科学版),2014,34(2):92-95.
[16]鲍杰,舒级.高阶广义2DGinzburg-Landau方程的随机吸引子[J].四川师范大学学学报(自然科学版),2014,37(5):298-306.
[17]彭冬冬,李扬荣.小噪音驱动的广义Ginzburg-Landau方程的随机吸引子的上半连续性[J].西南师范大学学报(自然科学版),2015,40(4):16-20.
[18]张凤,姜金平,王艳等.复系数Ginzburg-Landau方程的拉回吸引子[J].云南师范大学学报(自然科学版),2017,37(1),32-36.
[19]陈兆蕙,李泽华.三维非线性复Ginzburg-Landau方程的同宿波解[J].徐州师范大学学报(自然科学版),2012,30(1):14-17.
[20]高洪俊.广义Ginzburg-Landau方程组的有限维行为[J].应用数学学报,1998,21(4),481-491.
[21]张佳,舒级,董建等.具乘性噪音的广义Ginzburg-Landau方程的随机吸引子[J].四川师范大学学报(自然科学版),2015,38(5),638-643.
[22]林元烈.应用随机过程[M].北京:清华大学出版社,2002.
[23]ARNOLD L.Random dynamical system[M].Berlin:Springer-Verlag,1998.
[24]BALL J M.Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations[J].J Nonl.Sci.1997,7(5):475-502.
[25]TEMAN R.Infinite dimensional dynamical systems in mechanics and physics[M].Berlin:Springer-Verlag,1997.
[26]程其襄,张奠宇,魏国强,等.实变函数与泛函分析基础[M].北京:高等教育出版社,2007:170-288.
[2]金国华,曾志芳.(2+1)维变系数Nizhnik-Novikov-Veselov方程的孤子解[J].南昌大学学报(理科版),2015,39(3):229-231.
[3]万亮,龚雅玲,刘建国.广义Kuramoto-Sivashinsky方程的孤子解[J].南昌大学学报(理科版),2015,39(4):319-322.
[4]蒋燕.(2+1)维变系数Kadomtsev-Petviashvili方程新的精确解[J].南昌大学学报(理科版),2015,39(5):423-425.
[5]秦立春.广义双曲函数法求解(2+1)维变系数NizhnikNovikov-Veselov方程新的孤子解[J].南昌大学学报(理科版),2016,40(2):107-116.
[6]丁瑶.(2+1)维Potential Kadomtsev-Petviashvili方程新的精确解[J].南昌大学学报(理科版),2016,40(6):528-531.
[7]黄伟凡.(2+1)维破裂孤子方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(1):8-12.
[8]赵欢,邱震钰.(3+1)维破裂孤子方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(2):114-117.
[9]熊伟.(3+1)维Yu-Toda-Sasa-Fukuyama方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(3):211-215.
[10]袁娜.(3+1)维Boiti-Leon-Manna-Pempinelli方程新的三波解[J].南昌大学学报(理科版),2017,41(4):319-323.
[11]付中华,李良树.(G'/G)展开法求解(3+1)维JimboMiwa方程新的精确解[J].南昌大学学报(理科版),2017,41(5):418-422.
[12]秦立春.Caudrey-Dodd-Gibbon-Kaeada方程的新双周期孤子解[J].南昌大学学报(理科版),2017,41(6):524-526.
[13]莫春鹏,李栋龙.复Ginzburg-Landau方程整体解的存在性[J].广西工学院学报,2006,17(3):17-20.
[14]杨林,黄琼伟,戴正德.双核非线性光导纤维材料的整体吸引子[J].湖南大学学报(自然科学版),2009,25(3):12-16.
[15]王蕊,李扬荣.带有可乘白噪音的广义Ginzburg-Landau方程的随机吸引子[J].西南大学学报(自然科学版),2014,34(2):92-95.
[16]鲍杰,舒级.高阶广义2DGinzburg-Landau方程的随机吸引子[J].四川师范大学学学报(自然科学版),2014,37(5):298-306.
[17]彭冬冬,李扬荣.小噪音驱动的广义Ginzburg-Landau方程的随机吸引子的上半连续性[J].西南师范大学学报(自然科学版),2015,40(4):16-20.
[18]张凤,姜金平,王艳等.复系数Ginzburg-Landau方程的拉回吸引子[J].云南师范大学学报(自然科学版),2017,37(1),32-36.
[19]陈兆蕙,李泽华.三维非线性复Ginzburg-Landau方程的同宿波解[J].徐州师范大学学报(自然科学版),2012,30(1):14-17.
[20]高洪俊.广义Ginzburg-Landau方程组的有限维行为[J].应用数学学报,1998,21(4),481-491.
[21]张佳,舒级,董建等.具乘性噪音的广义Ginzburg-Landau方程的随机吸引子[J].四川师范大学学报(自然科学版),2015,38(5),638-643.
[22]林元烈.应用随机过程[M].北京:清华大学出版社,2002.
[23]ARNOLD L.Random dynamical system[M].Berlin:Springer-Verlag,1998.
[24]BALL J M.Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations[J].J Nonl.Sci.1997,7(5):475-502.
[25]TEMAN R.Infinite dimensional dynamical systems in mechanics and physics[M].Berlin:Springer-Verlag,1997.
[26]程其襄,张奠宇,魏国强,等.实变函数与泛函分析基础[M].北京:高等教育出版社,2007:170-288.