Averaging principle for Korteweg-de Vries equation with a random fast oscillation

被引:4
作者
Gao, Peng [1 ]
机构
[1] Northeast Normal Univ, Ctr Math & Interdisciplinary Sci, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
来源
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2019年 / 70卷 / 04期
关键词
Korteweg-de Vries equation; Averaging principle; Strong convergence; Fast-slow SPDEs; HYPERBOLIC-PARABOLIC EQUATIONS; STOCHASTIC KORTEWEG; STRONG-CONVERGENCE; DRIVEN; DEVIATION;
D O I
10.1007/s00033-019-1165-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This work concerns averaging principle for Korteweg-de Vries equation perturbed by a oscillating term which arises from the solution of a stochastic reaction-diffusion equation. This model can be translated into multiscale stochastic partial differential equations. Under some suitable conditions, we show that the slow component strongly converges to the solution of a single Korteweg-de Vries equation with a modified coefficient (averaged equation). To be more precise, by using the Khasminskii technique, we can obtain the strong convergence rate of the slow component towards the solution of the corresponding averaged equation, and as a consequence, the multiscale system can be reduced to the averaged equation.
引用
收藏
页数:28
相关论文
共 35 条