An integro-differential equation modelling a Newtonian dynamics and its scaling limit

• Verfasst von: Oelschläger, Karl [VerfasserIn]
• Titel: An integro-differential equation modelling a Newtonian dynamics and its scaling limit
• Verf.angabe: Karl Oelschläger
• Umfang: 36 S.
• Fussnoten: Gesehen am 08.06.2018
• Titel Quelle: Enthalten in: Archive for rational mechanics and analysis
• Jahr Quelle: 1997
• Band/Heft Quelle: 137(1997), 2, S. 99-134
• ISSN Quelle: 1432-0673
• DOI: doi:10.1007/s002050050024
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1576202534

Abstract

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.