2024/12/11 by Kuang Huang, Bangti Jin, Huang, Kuang +7 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Thermoelastic and Magnetoelastic Phenomena #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2412.08220
openalex publication_date 2024/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from a posteriori partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time and a general second-order elliptic operator in space. We establish the well-posedness of the direct problem in the sense of transposition and improved local regularity. Using classical unique continuation of the subdiffusion model and improved local solution regularity, we prove the uniqueness of simultaneously recovering the locations of point sources, time-dependent strengths and initial condition for both one- and multi-dimensional cases. Moreover, in the one-dimensional case, the elliptic operator can have time-dependent coefficients. These results extend existing studies on point source identification for parabolic type problems. Additionally we present several numerical experiments to show the feasibility of numerical reconstruction.