Simultaneous uniqueness for a coefficient inverse problem in one-dimensional fractional diffusion equation from an interior point measurement

2024/10/22 by Xiaohua Jing, Zhiyuan Li, Jing, Xiaohua +3
Mathematics · Computer Science · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2410.16808

Abstract

This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order α∈(0,1). We prove the uniqueness for the inverse problem by observation data at one interior point over a finite time interval, provided that a coefficient is known on a subinterval. Our proof is based on the uniqueness in the inverse spectracl problem for a Sturm-Liouville problem by means of the Weyl m-function and the spectral representation of the solution to an initial-boundary value problem for the fractional diffusion equation.

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