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

Zhang, Qi; Zhao, Huaizhong

Abstract

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.

Citation

Zhang, Q., & Zhao, H. (2022). Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations. Journal of Differential Equations, 331, 1-49. https://doi.org/10.1016/j.jde.2022.05.015

• Journal Article Type: Article
• Acceptance Date: May 15, 2022
• Online Publication Date: May 25, 2022
• Publication Date: Sep 15, 2022
• Deposit Date: May 27, 2022
• Publicly Available Date: May 27, 2022
• Journal: Journal of Differential Equations
• Print ISSN: 0022-0396
• Electronic ISSN: 1090-2732
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 331
• Pages: 1-49
• DOI: https://doi.org/10.1016/j.jde.2022.05.015
• Public URL: https://durham-repository.worktribe.com/output/1204165