Autor(en): | Duong, Manh Hong Lamacz, Agnes Peletier, Mark A. Sharma, Upanshu |
Titel: | Variational approach to coarse-graining of generalized gradient flows |
Sprache (ISO): | en |
Zusammenfassung: | In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational evolutions, and which often arises from a large-deviations principle. It has three main features: (A) a natural interaction between the duality structure and the coarse-graining, (B) application to systems with non-dissipative effects, and (C) application to coarse-graining of approximate solutions which solve the equation only to some error. As examples, we use this technique to solve three limit problems, the overdamped limit of the Vlasov-Fokker-Planck equation and the small-noise limit of randomly perturbed Hamiltonian systems with one and with many degrees of freedom. |
URI: | http://hdl.handle.net/2003/34189 http://dx.doi.org/10.17877/DE290R-16268 |
Erscheinungsdatum: | 2015-08-04 |
Enthalten in den Sammlungen: | Preprints der Fakultät für Mathematik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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Preprint 2015-07.pdf | 805.46 kB | Adobe PDF | Öffnen/Anzeigen |
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