An inverse problem for a fractional diffusion equation with fractional power type nonlinearities

TL;DR

This paper investigates the inverse problem of identifying fractional power nonlinearities in a fractional diffusion equation using exterior measurements, employing linearization and approximation techniques.

Contribution

It introduces a novel method to determine fractional power nonlinearities from partial boundary data in fractional diffusion equations.

Findings

Successful determination of nonlinearities from exterior measurements.

Application of linearization and Runge approximation in the fractional setting.

Establishment of well-posedness for the inverse problem.

Abstract

We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map. Our arguments are based on a first order linearization as well as the parabolic Runge approximation property.