Uniqueness and non-uniqueness for an inverse source problem of a distributed order time-fractional diffusion equation
Year: 2026
Type: article
Abstract: We investigate an inverse source problem for a distributed order time-fractional diffusion equation involving a fractional elliptic operator. The objective is to determine simultaneously the initial datum and a spatially dependent source term. We show that a single measurement at a fixed time is insufficient to guarantee uniqueness, even when observations are available over the entire spatial domain. In contrast, we establish a conditional uniqueness result showing that two measurements taken at distinct time instants uniquely determine both unknowns from a proper subdomain, under a non-resonance condition and a unique continuation assumption on the states at the observation times. The results highlight the essential role of temporal diversity in restoring identifiability under partial spatial observations.
Source: Applied Mathematics Letters
Author: Dinh Nguyen Duy Hai
Institution: Ho Chi Minh University of Banking
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,800
OpenAlex ID: W7154473889