Convergence of discrete Aubry-Mather model in the continuous limit
| hal.structure.identifier | Beijing Normal University [BNU] | |
| dc.contributor.author | SU, Xifeng | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | THIEULLEN, Philippe | |
| dc.date.accessioned | 2024-04-04T03:05:14Z | |
| dc.date.available | 2024-04-04T03:05:14Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 0951-7715 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193227 | |
| dc.description.abstractEn | We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions. | |
| dc.language.iso | en | |
| dc.publisher | IOP Publishing | |
| dc.subject.en | discrete weak KAM theory | |
| dc.subject.en | Frenkel-Kontorova models | |
| dc.subject.en | AubryMather theory | |
| dc.subject.en | discounted Lax-Oleinik operator | |
| dc.subject.en | ergodic cell equation | |
| dc.subject.en | shortrange interactions | |
| dc.subject.en | additive eigenvalue problem | |
| dc.title.en | Convergence of discrete Aubry-Mather model in the continuous limit | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1088/1361-6544/aaacbb | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Nonlinearity | |
| bordeaux.volume | 31 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 5 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01869517 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01869517v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Nonlinearity&rft.date=2018&rft.volume=31&rft.issue=5&rft.eissn=0951-7715&rft.issn=0951-7715&rft.au=SU,%20Xifeng&THIEULLEN,%20Philippe&rft.genre=article |
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