Direct and Inverse Source Problem for a Space Fractional Advection Dispersion Equation

TL;DR

This paper investigates direct and inverse problems for a space fractional advection-dispersion equation, establishing fundamental solutions, linear relations, well-posedness, and providing numerical illustrations.

Contribution

It introduces a comprehensive analysis of both direct and inverse problems for space fractional equations, including fundamental solutions and stability results.

Findings

Linear relation between source and observation

Well-posedness established for both problems

Numerical example demonstrating theoretical results

Abstract

In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from a final observation. We first drive the fundamental solution to the direct problem and we show that the relation between source and the final observation is linear. Moreover, we study the well-posedness of both problems: existence, uniqueness and stability. Finally, we illustrate the results with a numerical example.