Simultaneous Identification of Coefficients and Source in a Subdiffusion Equation from One Passive Measurement

TL;DR

This paper develops a method to uniquely identify coefficients and a source term in a subdiffusion equation from a single passive measurement, combining theoretical analysis with a reconstruction algorithm and numerical validation.

Contribution

It introduces new uniqueness results for simultaneous parameter and source identification in fractional diffusion equations, extending to multidimensional cases under symmetry.

Findings

Uniqueness of parameter and source identification established.

Reconstruction algorithm demonstrated through numerical simulations.

Extension of results to multidimensional settings with symmetry assumptions.

Abstract

This article is devoted to the detection of parameters in anomalous diffusion from a single passive measurement. More precisely, we consider the simultaneous identification of coefficients as well as a time-dependent source term appearing in a time-fractional diffusion equation from a single boundary or internal passive measurement. We obtain several uniqueness results in dimension one as well as a multidimensional extension under some symmetry assumptions. Our analysis relies on spectral representation of solutions, complex and harmonic analysis combined with some known inverse spectral results for Sturm-Liouville operators. The theoretical results are complemented by a corresponding reconstruction algorithm and numerical simulations.