Geodesic
On the formulation of initial-value problems for systems consisting of relativistic particles
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 211-226.

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We discuss questions related to the well-posedness of problems on the motion of relativistic many-body systems. For one-dimensional relativistic motion of $N$ similar charges, we prove that an ordinary Cauchy problem usual in Newton mechanics can be stated; this is done in the framework of microscopic Maxwell–Lorentz electrodynamics (including a model with self-action) or Wheeler–Feynman theory. 
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S. B. Kirpichev; P. A. Polyakov. On the formulation of initial-value problems for systems consisting of relativistic particles. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 211-226. http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a9/

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