Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 박진영 | - |
dc.date.accessioned | 2019-05-28T02:37:33Z | - |
dc.date.available | 2019-05-28T02:37:33Z | - |
dc.date.issued | 2017-01 | - |
dc.identifier.citation | JOURNAL OF DIFFERENTIAL EQUATIONS, v. 262, no. 2, page. 978-1022 | en_US |
dc.identifier.issn | 0022-0396 | - |
dc.identifier.issn | 1090-2732 | - |
dc.identifier.uri | https://www.sciencedirect.com/science/article/pii/S0022039616303291?via%3Dihub | - |
dc.identifier.uri | https://repository.hanyang.ac.kr/handle/20.500.11754/106086 | - |
dc.description.abstract | The Kuramoto model is a prototype phase model describing the synchronous behavior of weakly coupled limit-cycle oscillators. When the number of oscillators is sufficiently large, the dynamics of Kuramoto ensemble can be effectively approximated by the corresponding mean-field equation, namely "the Kuramoto-Sakaguchi (KS) equation". This KS equation is a kind of scalar conservation law with a nonlocal flux function due to the mean-field interactions among oscillators. In this paper, we provide a unique global solvability of bounded variation (BV) weak solutions to the kinetic KS equation for identical oscillators using the method of front-tracking in hyperbolic conservation laws. Moreover, we also show that our BV weak solutions satisfy local-in-time L-1-stability with respect to BV-initial data. For the ensemble of identical Kuramoto oscillators, we explicitly construct an exponentially growing BV weak solution generated from BV perturbation of incoherent state for any positive coupling strength. This implies the nonlinear instability of incoherent state in a positive coupling strength regime. We provide several numerical examples and compare them with our analytical results. (C) 2016 Elsevier Inc. All rights reserved. | en_US |
dc.description.sponsorship | The work of D. Amadori is partially supported by the Miur-PRIN 2012 Project Nonlinear Hyperbolic Partial Differential Equations, Dispersive and Transport Equations: theoretical and applicative aspects. The work of S.-Y. Ha is partially supported by a National Research Foundation of Korea Grant (2014R1A2A2A05002096) funded by the Korean government, and the work of J. Park was supported by NRF (National Research Foundation of Korea) Grant funded by the Korean Government (NRF-2014-Fostering Core Leaders of the Future Basic Science Program). | en_US |
dc.language.iso | en | en_US |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | en_US |
dc.subject | BV weak solution | en_US |
dc.subject | Continuous dependence | en_US |
dc.subject | The Kuramoto model | en_US |
dc.subject | The Kuramoto-Sakaguchi equation | en_US |
dc.subject | Synchronization | en_US |
dc.title | On the global well-posedness of BV weak solutions to the Kuramoto-Sakaguchi equation | en_US |
dc.type | Article | en_US |
dc.relation.no | 2 | - |
dc.relation.volume | 262 | - |
dc.identifier.doi | 10.1016/j.jde.2016.10.004 | - |
dc.relation.page | 978-1022 | - |
dc.relation.journal | JOURNAL OF DIFFERENTIAL EQUATIONS | - |
dc.contributor.googleauthor | Amadori, Debora | - |
dc.contributor.googleauthor | Ha, Seung-Yeal | - |
dc.contributor.googleauthor | Park, Jinyeong | - |
dc.relation.code | 2017000500 | - |
dc.sector.campus | S | - |
dc.sector.daehak | COLLEGE OF NATURAL SCIENCES[S] | - |
dc.sector.department | DEPARTMENT OF MATHEMATICS | - |
dc.identifier.pid | jinyeongpark | - |
dc.identifier.orcid | http://orcid.org/0000-0002-1390-2623 | - |
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