Inverse source problems in transport equations with external forces

TL;DR

This paper investigates the inverse source problem in transport equations with external forces, establishing unique solvability and stability under generic conditions using advanced mathematical tools.

Contribution

It provides new results on the unique solvability and stability of inverse source problems in transport equations with external forces, employing Fredholm theory and Santalo's formula.

Findings

Unique solvability of direct and inverse problems for generic coefficients

Derivation of stability estimates for the inverse source

Application of Fredholm theorem and Santalo's formula in analysis

Abstract

This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular, for inverse problems, generic injectivity and a stability estimate of the source are derived. The analysis employs the Fredholm theorem and the Santalo's formula.