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
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页码：1 / 49
页数：49
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