dc.contributor.author | Galtung, Sondre Tesdal | |
dc.contributor.author | Raynaud, Xavier | |
dc.date.accessioned | 2021-04-30T09:05:59Z | |
dc.date.available | 2021-04-30T09:05:59Z | |
dc.date.created | 2021-04-22T14:53:29Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Nonlinearity. 2021, 34 (4), 2220-2274. | en_US |
dc.identifier.issn | 0951-7715 | |
dc.identifier.uri | https://hdl.handle.net/11250/2740531 | |
dc.description.abstract | We define a kinetic and a potential energy such that the principle of stationary action from Lagrangian mechanics yields a Camassa–Holm system (2CH) as the governing equations. After discretizing these energies, we use the same variational principle to derive a semi-discrete system of equations as an approximation of the 2CH system. The discretization is only available in Lagrangian coordinates and requires the inversion of a discrete Sturm–Liouville operator with time-varying coefficients. We show the existence of fundamental solutions for this operator at initial time with appropriate decay. By propagating the fundamental solutions in time, we define an equivalent semi-discrete system for which we prove that there exists unique global solutions. Finally, we show how the solutions of the semi-discrete system can be used to construct a sequence of functions converging to the conservative solution of the 2CH system. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | IOP Publishing | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | A semi-discrete scheme derived from variational principles for global conservative solutions of a Camassa–Holm system | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | publishedVersion | en_US |
dc.source.pagenumber | 2220-2274 | en_US |
dc.source.volume | 34 | en_US |
dc.source.journal | Nonlinearity | en_US |
dc.source.issue | 4 | en_US |
dc.identifier.doi | 10.1088/1361-6544/abc101 | |
dc.identifier.cristin | 1905890 | |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |