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.
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.
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|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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