An inverse problem for the fractional porous medium equation

TL;DR

This paper addresses an inverse problem for a fractional porous medium equation with variable coefficients, aiming to recover conductivity and absorption coefficients from partial boundary measurements using advanced mathematical techniques.

Contribution

It introduces a novel method combining a time-integral transform and unique continuation to solve the inverse problem for fractional porous medium equations with variable coefficients.

Findings

Successfully determines conductivity and absorption coefficients from exterior measurements

Develops a new approach leveraging fractional operator properties

Establishes uniqueness results for the inverse problem

Abstract

We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient from exterior partial measurements of the Dirichlet-to-Neumann map. Our approach relies on a time-integral transform technique as well as the unique continuation property of the fractional operator.