一类随机Burgers方程的奇摄动解
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摘要
讨论了一类随机Burgers方程的奇摄动解,其噪声项服从弱噪声Ornstein-Uhlenbeck(O-U)过程,并构造了相应的形式渐近解.通过摄动分析得到波的期望和初值条件,并通过余项估计得到渐近解的有效性.
In this paper,the singular perturbation solution for a class of stochastic burgers equation is discussed.Its volatility is subject to the weak noise Ornstein-Uhlenbeck(O-U)process.The corresponding asymptotic solution is constructed.By the perturbation analysis,the wave expectation v(t,x)and the initial condition g(t,x)are obtained.And the uniformly valid estimate for the asymptotic solution of the system is obtained.
In this paper,the singular perturbation solution for a class of stochastic burgers equation is discussed.Its volatility is subject to the weak noise Ornstein-Uhlenbeck(O-U)process.The corresponding asymptotic solution is constructed.By the perturbation analysis,the wave expectation v(t,x)and the initial condition g(t,x)are obtained.And the uniformly valid estimate for the asymptotic solution of the system is obtained.
引文
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[5]VILLARROEL J.The Stochastic Burger’s Equation in Ito’s Sense[J].Studies in Applied Mathematics,2004,112(1):87-100.
[6]VILLARROEL J.Stochastic Perturbations of Line Solitons of KP[J].Theoretical and Mathematical Physics,2003,137(3):1753-1765.
[7]司曲斯.随机微分方程理论及其应用[M].上海:上海科学技术文献出版社,1986:102-120.
[8]伍卓群,尹景学,王春朋.椭圆与抛物型方程引论[M].北京:科学出版社,2003:44-85.
[2]LILLO S D.The Burgers equation under multiplicative noise[J].Physics Letters A,1994,188(4/5/6):305-308.
[3]CHEKHLOV A,YAKHOT V.Kolmogorov turbulence in a random-force-driven Burgers equation[J].Physical Review E Statistical Physics Plasmas Fluids&Related Interdisciplinary Topics,1995,51(4):5681-5684.
[4]Weinane,Eric Vanden Eignden.Statistical Theory for the Stochastic Burgers Equation in the Inviscid Limit[J].Communications on Pure and Applied Mathematics,2000,53(7):852-901.
[5]VILLARROEL J.The Stochastic Burger’s Equation in Ito’s Sense[J].Studies in Applied Mathematics,2004,112(1):87-100.
[6]VILLARROEL J.Stochastic Perturbations of Line Solitons of KP[J].Theoretical and Mathematical Physics,2003,137(3):1753-1765.
[7]司曲斯.随机微分方程理论及其应用[M].上海:上海科学技术文献出版社,1986:102-120.
[8]伍卓群,尹景学,王春朋.椭圆与抛物型方程引论[M].北京:科学出版社,2003:44-85.