dc.contributor.author | Arnesen, Mathias Nikolai | |
dc.date.accessioned | 2020-04-03T09:45:52Z | |
dc.date.available | 2020-04-03T09:45:52Z | |
dc.date.created | 2019-09-06T14:58:56Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | Advances in Differential Equations. 2019, 24 (5-6), 257-282. | en_US |
dc.identifier.issn | 1079-9389 | |
dc.identifier.uri | https://hdl.handle.net/11250/2650261 | |
dc.description.abstract | We consider the Cauchy problem ∂tu + u∂xu + L(∂xu) = 0, u(0, x) = u0(x) for a class of Fourier multiplier operators L, and prove that the solution map u0 7→ u(t) is not uniformly continuous in Hs on the real line or on the torus for s > 3 2 . Under certain assumptions, the result also hold for s > 0. The class of equations considered includes in particular the Whitham equation and fractional Korteweg-de Vries equations and we show that, in general, the flow map cannot be uniformly continuous if the dispersion of L is weaker than that of the KdV operator. The result is proved by constructing two sequences of solutions converging to the same limit at the initial time, while the distance at a later time is bounded below by a positive constant. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Khayyam Publishing | en_US |
dc.title | Non-uniform dependence on initial data for equations of Whitham type | en_US |
dc.type | Journal article | en_US |
dc.description.version | submittedVersion | en_US |
dc.source.pagenumber | 257-282 | en_US |
dc.source.volume | 24 | en_US |
dc.source.journal | Advances in Differential Equations | en_US |
dc.source.issue | 5-6 | en_US |
dc.identifier.cristin | 1722389 | |
dc.description.localcode | This article will not be available due to copyright restrictions (c) 2019 by Khayyam Publishing | en_US |
cristin.unitcode | 194,63,15,0 | |
cristin.unitname | Institutt for matematiske fag | |
cristin.ispublished | true | |
cristin.fulltext | preprint | |
cristin.qualitycode | 1 | |