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An integro-differential equation modelling a Newtonian dynamics and its scaling limit. (English) Zbl 0880.70007
Summary: We consider an integro-differential equation describing a Newtonian dynamics with long-range interaction for a continuous distribution of mass in ${\bold R}$. 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.

70F99Dynamics of a system of particles
45K05Integro-partial differential equations
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