Carleman estimates for space semi-discrete approximations of one-dimensional stochastic parabolic equation and its applications

被引：0
作者：
Wu, Bin [1 ,2 ]
Wang, Ying [1 ]
Wang, Zewen [3 ,4 ]
机构：
[1] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Peoples R China
[2] Nanjing Univ Informat Sci & Technol, Ctr Appl Math Jiangsu Prov, Nanjing 210044, Peoples R China
[3] Guangzhou Maritime Univ, Sch Arts & Sci, Guangzhou 510725, Peoples R China
[4] East China Univ Technol, Sch Sci, Nanchang 330013, Peoples R China
来源：
INVERSE PROBLEMS | 2024年 / 40卷 / 11期
基金：
中国国家自然科学基金;
关键词：
Carleman estimates; inverse random source problem; Cauchy problem; space semi-discrete stochastic parabolic equation; NULL CONTROLLABILITY; ARBITRARY DIMENSION; ELLIPTIC-OPERATORS; INVERSE PROBLEMS;
D O I：
10.1088/1361-6420/ad7d2f
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study discrete Carleman estimates for space semi-discrete approximations of one-dimensional stochastic parabolic equation. We then apply these Carleman estimates to investigate two inverse problems for the space semi-discrete stochastic parabolic equations, including a discrete inverse random source problem and a discrete Cauchy problem. We firstly establish two Carleman estimates for a one-dimensional semi-discrete stochastic parabolic equation, one for homogeneous boundary and the other for non-homogeneous boundary. Then we apply these two estimates separately to derive two stability results. The first one is the Lipschitz stability for the discrete inverse random source problem. The second one is the H & ouml;lder stability for the discrete Cauchy problem.
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页数：33
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