Work

Conditional Stability and Numerical Reconstruction of a Parabolic Inverse Source Problem Using Carleman Estimates

Year: 2025

Type: preprint

Abstract: In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and Hölder stability for the inverse problem with and without boundary conditions, respectively, using suitable Carleman estimates. Then we propose a numerical approach for solving the inverse problem using conforming finite element approximations in both time and space. Moreover, by utilizing the conditional stability estimates, we prove rigorous error bounds on the discrete approximation. We present several numerical experiments to illustrate the effectiveness of the approach.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2508.15406

Authors: Hu, Tianhao, Huang, Xinchi, Jin, Bangti, Quan, Qimeng, Zhou, Zhi

Institutions: Chinese University of Hong Kong, The University of Tokyo

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, National Natural Science Foundation of China, Chinese University of Hong Kong

Awards: G2574649659, G5057519578

OpenAlex ID: W4416050996

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