Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations

被引：1

作者：

Zhang, Qi ^{[1
,2
]}

Zhao, Huaizhong ^{[3
,4
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Fudan Univ, Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China

[3] Univ Durham, Dept Math Sci, Durham DH1 3LE, England

[4] Shandong Univ, Res Ctr Math & Interdisciplinary Sci, Qingdao 266237, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 331卷

基金：

国家重点研发计划; 中国国家自然科学基金; 英国工程与自然科学研究理事会;

关键词：

Stochastic partial differential equations; Mass-conservative; Backward doubly stochastic differential; equations; Neumann boundary condition; Stationary solution; Stochastic Allen-Cahn equation; SPDES; CALCULUS; MOTION;

D O I：

10.1016/j.jde.2022.05.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we first study the connection between mass-conserving SPDEs on a bounded domain and backward doubly stochastic differential equations, which is a new extension of nonlinear Feynman-Kac formula to mass-conserving SPDEs. Then the infinite horizon mass-conserving SPDEs and their stationary solutions are considered without monotonic conditions, while the Poincare inequality plays an important role. Finally, the existence and the stationarity to solutions of non-Lipschitz mass-conserving stochastic Allen-Cahn equations are obtained. (c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license

引用

页码：1 / 49

页数：49

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