# Well-posedness of the Goursat problem and stability for point source inverse backscattering

## TL;DR

This paper establishes well-posedness and stability results for the point source inverse backscattering problem, demonstrating logarithmic stability under angular control and H"older stability for radial symmetry, with novel well-posedness proofs for related equations.

## Contribution

It provides new well-posedness results for the Goursat problem and the point source equation, crucial for proving stability in inverse backscattering.

## Key findings

- Logarithmic stability under angular control
- H"older stability for radial symmetry
- Well-posedness of the Goursat problem

## Abstract

We show logarithmic stability for the point source inverse backscattering problem under the assumption of angularly controlled potentials. Radial symmetry implies H\"older stability. Importantly, we also show that the point source equation is well-posed and also that the associated characteristic initial value problem, or Goursat problem, is well-posed. These latter results are difficult to find in the literature in the form required by the stability proof.