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

Zhang, Qi; Zhao, Huaizhong

doi:10.1016/j.jde.2022.05.015

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

Zhang, Qi; Zhao, Huaizhong

Authors

Qi Zhang

Professor Huaizhong Zhao huaizhong.zhao@durham.ac.uk
Professor

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
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	331
Pages	1-49
DOI	https://doi.org/10.1016/j.jde.2022.05.015

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Copyright 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/).