  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.
