有界区间上的随机广义非局部Burgers方程鞅解的存在性  

The Existence of Martingale Solution for a Stochastic Generalized Nonlocal Burgers Equation on Bounded Intervals

作　　者：何兴[1] 陈光淦[1] 杨欢[1] HE Xing CHEN Guanggan YANG Huan(College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan)

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2016年第6期809-814,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11571245和11401409);四川省教育厅重点科研项目(15ZA0031)

摘　　要：研究有界区域上随机广义非局部Burgers方程.通过在适当的加权空间上考虑,克服了有界区域上非局部Laplace算子带来的困难.运用一系列精致估计获得了系统的某些有界性.利用胎紧代替噪声给系统带来的通常意义下的紧性问题,最终获得系统鞅解的存在性.This paper is concerned with the stochastic generalized nonlocal Burgers equation on bounded intervals.Introducing a weighted sobolev space,it overcomes the difficulties which are caused by the nonlocal Laplacian operator on bounded domains.By using a series of precise estimates,the boundedness of the system is established.Using the tightness to solve the general compact problem which is caused by noise,it finally obtains the existence of martingale solutions for the system.

关 键 词：随机广义Burgers方程 有界区域 非局部Laplace算子 鞅解 

分 类 号：O175.2[理学—数学]