Work

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

Year: 2024

Type: article

Abstract: 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 Hölder stability for the discrete Cauchy problem.

Source: Inverse Problems

DOI: 10.1088/1361-6420/ad7d2f

Authors: Bin Wu, Ying Wang, Zewen Wang

Institutions: Nanjing University of Information Science and Technology, East China University of Technology

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Jiangxi Province

Awards: G5265679361, G535366209, G7003339846