Collinear n-body problem of classical electrodynamics
One model for the motion of n charged particles on the x-axis leads to a system of delay differential equations with delays that depend on the unknown trajectories. If appropriate past histories of the trajectories are given, say on (-r,0), then for sufficiently small t greater than or equal to 0 one has a system of n/sup 2/ ordinary differential equations of the form y' = f(t,y) with y(0) = y/sub 0/ given. The function f, which involves the known past histories of the trajectories, is continuous; thus, existence of solutions is assured. However, f does not satisfy the Lipschitz condition usually used for proving uniqueness. The main new result is that the solution of the above equation is unique provided.
- Research Organization:
- Rhode Island Univ., Kingston (USA); Sandia National Labs., Albuquerque, NM (USA)
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 5293218
- Report Number(s):
- SAND-80-1235C; CONF-800634-1
- Resource Relation:
- Conference: International conference on nonlinear phenomena in mathematical sciences, Arlington, TX, USA, 16 Jun 1980
- Country of Publication:
- United States
- Language:
- English
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