An integro-differential equation modelling a Newtonian dynamics and its scaling limit
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...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
June 1997
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| In: |
Archive for rational mechanics and analysis
Year: 1997, Volume: 137, Issue: 2, Pages: 99-134 |
| ISSN: | 1432-0673 |
| DOI: | 10.1007/s002050050024 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s002050050024 Verlag, Volltext: https://link.springer.com/article/10.1007/s002050050024 
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| Author Notes: | Karl Oelschläger |
| Summary: | 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. |
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| Item Description: | Gesehen am 08.06.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1432-0673 |
| DOI: | 10.1007/s002050050024 |