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Bauer, G.; Deckert, D.-A.; Dürr, D. and Hinrichs, G. (2017): Global solutions to the electrodynamic two-body problem on a straight line. In: Zeitschrift für Angewandte Mathematik und Physik, Vol. 68, No. 3

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The classical electrodynamic two-body problem has been a long standing open problem in mathematics. For motion constrained to the straight line, the interaction is similar to that of the two-body problem of classical gravitation. The additional complication is the presence of unbounded state-dependent delays in the Coulomb forces due to the finiteness of the speed of light. This circumstance renders the notion of local solutions meaningless, and therefore, straightforward ODE techniques cannot be applied. Here, we study the time-symmetric case, i.e., the Fokker-Schwarzschild-Tetrode (FST) equations, comprising both advanced and retarded delays. We extend the technique developed in Deckert and Hinrichs (J Differ Equ 260: 6900-6929, 2016), where existence of FST solutions was proven on the half line, to ensure global existence-a result that had been obtained by Bauer (Ein Existenzsatz fur die Wheeler-Feynman-Elektrodynamik, Herbert Utz Verlag, Munchen, 1997). Due to the novel technique, the presented proof is shorter and more transparent but also relies on the idea to employ asymptotic data to characterize solutions.

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