Martingale and weak solutions for a stochastic nonlocal Burgers equation on finite intervals

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• 作者：Guangying Lv^a ; ^{gylvmaths@henu.edu.cn} ; Jinqiao Duan^b ; ^duan@iit.edu
• 关键词：Itô ; 's formula ; Stochastic Burgers equation ; Nonlocal Burgers equation ; Prokhorov's theorem ; Skorokhod's embedding theorem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：176-194
• 全文大小：414 K
• 卷排序：449

文摘

This work is about the existence of martingale solutions and weak solutions for a stochastic nonlocal Burgers equation on a one dimensional bounded domain. The existence of a martingale solution is shown by using a Galerkin approximation, Prokhorov's theorem and Skorokhod's embedding theorem. The same Galerkin approximation also leads to the existence of weak solution for the corresponding deterministic nonlocal Burgers equation on a bounded domain.