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Variational approach to coarse-graining of generalized gradient flows
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Duong, Manh Hong, Lamacz, Agnes, Peletier, Mark A. and Sharma, Upanshu (2017) Variational approach to coarse-graining of generalized gradient flows. Calculus of Variations and Partial Differential Equations, 56 . 100 . ISSN 0944-2669.
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Official URL: https://doi.org/10.1007/s00526-017-1186-9
Abstract
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.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Large deviations, Hamiltonian systems | |||||||||
| Journal or Publication Title: | Calculus of Variations and Partial Differential Equations | |||||||||
| Publisher: | Springer | |||||||||
| ISSN: | 0944-2669 | |||||||||
| Official Date: | August 2017 | |||||||||
| Dates: |
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| Volume: | 56 | |||||||||
| Article Number: | 100 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 29 June 2017 | |||||||||
| Date of first compliant Open Access: | 22 January 2018 | |||||||||
| RIOXX Funder/Project Grant: |
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