On the existence of scattering solutions for the Abraham-Lorentz-Dirac equation

It is well known that, in the presence of an attractive force having a Coulomb singularity, scattering solutions of the nonrelativistic Abraham--Lorentz--Dirac equation having nonrunaway character do not exist, for the case of motions on the line. By numerical computations on the full three dimensional case, we give indications that indeed there exists a full tube of initial data for which nonrunay solutions of scatterig type do not exist. We also give a heuristic argument which allows to estimate the size of such a tube of initial data. The numerical computations also show that in a thin region beyond such a tube one has the nonuniqueness phenomenon, i.e. the "mechanical'' data of position and velocity do not uniquely determine the nonrunaway trajectory.