Uniqueness for inverse source problems for fractional diffusion-wave equations by data during not acting time. (1st February 2023)

• Record Type: Journal Article
• Authors: Yamamoto, M
• Is Part Of: Inverse problems. Volume 39:Number 2(2023)
• Publication Date: 2023-02-01
• Subjects: fractional diffusion-wave equation -- inverse source problem -- uniqueness; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aca55c
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider fractional diffusion-wave equations with source term which is represented in a form of a product of a temporal function and a spatial function. We prove the uniqueness for inverse source problem of determining spatially varying factor by decay of data as the time tends to ∞, provided that the source does not work during the observation. Our main result asserts the uniqueness if data decay more rapidly than 1 t p with any p ∈ N as t → ∞ . Data taken not from the initial time are realistic but the uniqueness is not known in general. The proof is based on the analyticity and the asymptotic behavior of a function generated by the solution.