Stability for some inverse problems for transport equations

TL;DR

This paper establishes stability estimates for inverse problems involving determining source terms and coefficients in first-order PDEs, using minimal boundary data and relaxed conditions on the principal part.

Contribution

It provides new conditional stability results for inverse transport problems with less restrictive boundary data and assumptions.

Findings

Proves stability estimates with minimal boundary observations.

Relaxes conditions on the principal part of the PDE.

Addresses inverse problems for first-order transport equations.

Abstract

In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed condition on the principal part.