Uniqueness for an inverse problem for a semilinear time-fractional diffusion equation

TL;DR

This paper investigates the uniqueness of solutions for an inverse problem involving a semilinear time-fractional diffusion equation, utilizing a positivity principle and integral data over time.

Contribution

It introduces a new approach to prove uniqueness in inverse problems for fractional diffusion equations using a positivity principle.

Findings

Proved the uniqueness of the inverse problem solution.

Established a positivity principle for the differential equation.

Demonstrated the method's effectiveness with integral time data.

Abstract

An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution of the inverse problem is studied. The method uses a positivity principle of the corresponding differential equation that is also proved in the paper.