The global uniqueness of a dissipative fractional Helmholtz equation

Yu Zhang and Wenjing Zhang

Chaos, Solitons & Fractals, 2024, vol. 188, issue C

Abstract: In this paper, we consider the Dirichlet problem for the fractional Helmholtz equation with dissipation, and study the inverse problem of determining the source function, potential function and dissipation of the equation using the Dirichlet-to-Neumann map and Runge approximation. We prove the global uniqueness of these three functions of the equation under low-frequency conditions. As the main result, this implies that one can use the external data to uniquely recover the unknown functions of the equation in the low-frequency case, which will be of great significance in photoacoustic tomography and thermoacoustic tomography.

Keywords: Dirichlet-to-Neumann map; Low-frequency asymptotics; Runge approximation property (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010646

DOI: 10.1016/j.chaos.2024.115512

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