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

Zhang, Qi and Zhao, Huaizhong (2022) 'Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations.', Journal of Differential Equations, 331 . pp. 1-49.

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.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.jde.2022.05.015
Publisher statement:© 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Date accepted:15 May 2022
Date deposited:27 May 2022
Date of first online publication:25 May 2022
Date first made open access:27 May 2022

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