Archive for Rational Mechanics and Analysis

, Volume 137, Issue 2, pp 99–134

An Integro-Differential Equation Modelling a Newtonian Dynamics and Its Scaling Limit

  • Karl Oelschläger

DOI: 10.1007/s002050050024

Cite this article as:
Oelschläger, K. Arch Rational Mech Anal (1997) 137: 99. doi:10.1007/s002050050024


We consider an integro-differential equation describing a Newtonian dynamics with long-range interaction for a continuous distribution of mass in R. First, we deduce unique existence and regularity properties of its solution locally in time, and then we investigate a scaling limit. As limit dynamics a nonlinear wave equation is determined. Technically, we rely on the connection of the Newtonian dynamics to a system of an integro-differential equation and a partial differential equation. Basic for our considerations is the study of the regularity properties of the solution of that system. For that purpose we exploit its similarity to a certain strongly hyperbolic system of partial differential equations.

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Karl Oelschläger
    • 1
  1. 1.Institut für Angewandte Mathematik Universität Heidelberg Im Neuenheimer Feld 294 D - 69120 HeidelbergXX