Abstract:This article investigates the exact controllability of three-dimensional stochastic Maxwell equations, a coupled system comprising two stochastic partial differential equations. The research establishes the observability inequality for the backward stochastic Maxwell equations using the multiplier method, and subsequently, proves the exact controllability of the forward equations. The control acting on the diffusion term is found to be indispensable, since exact controllability is destroyed when this control is removed; it is further proved that the controllability result obtained in this paper is achieved with a minimal number of controls. Finally, a numerical algorithm combining a central difference for spatial discretization, a midpoint scheme for temporal discretization and Lagrange multiplier method is proposed, yielding numerical results that offer the control value and lead to deeper insights into the underlying theoretical framework.
| Subjects: | Optimization and Control (math.OC) |
| Cite as: | arXiv:2605.25932 [math.OC] |
| (or arXiv:2605.25932v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25932 arXiv-issued DOI via DataCite (pending registration) |
From: Liying Sun [view email]
[v1]
Mon, 25 May 2026 15:13:32 UTC (1,218 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。