An inverse problem of determining fractional orders in a fractal solute transport model

TL;DR

This paper investigates an inverse problem in a fractal solute transport model, aiming to determine fractional orders using interior measurements, and demonstrates solution uniqueness and numerical stability through Laplace transform techniques.

Contribution

It introduces a novel inverse problem for fractional orders in a fractal transport model and proves solution uniqueness and stability with numerical validation.

Findings

Unique solution existence for the forward problem.

Proof of inverse problem's uniqueness in real space.

Numerical inversions showing stability with noisy data.

Abstract

A fractal mobile-immobile (MIM in short) solute transport model in porous media is set forth, and an inverse problem of determining the fractional orders by the additional measurements at one interior point is investigated by Laplace transform. The unique existence of the solution to the forward problem is obtained based on the inverse Laplace transform, and the uniqueness of the inverse problem is proved in the real-space of Laplace transform by the maximum principle, and numerical inversions with noisy data are presented to demonstrate a numerical stability of the inverse problem.