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Existence and stability of regularized shock solutions, with applications to rimming flows

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dc.contributor.authorBenilov, E. S.
dc.contributor.authorBenilov, M. S.
dc.contributor.authorO’Brien, S. B. G.
dc.date.accessioned2022-08-31T10:45:41Z
dc.date.available2022-08-31T10:45:41Z
dc.date.issued2008
dc.description.abstractThis paper is concerned with regularization of shock solutions of nonlinear hyperbolic equations, i.e., introduction of a smoothing term with a coefficient ε, then taking the limit ε → 0. In addition to the classical use of regularization for eliminating physically meaningless solutions which always occur in non-regularized equa tions (e.g. waves of depression in gas dynamics), we show that it is also helpful for stability analysis. The general approach is illustrated by applying it to rimming flows, i.e., flows of a thin film of viscous liquid on the inside of a horizontal rotating cylinder, with or without surface tension (which plays the role of the regularizing effect). In the latter case, the spectrum of available linear eigenmodes appears to be continuous, but in the former, it is discrete and, most importantly, remains discrete in the limit of infinitesimally weak surface tension. The regularized (discrete) spectrum is fully determined by the point where the velocity of small perturbations vanishes, with the rest of the domain, including the shock region, being unimportant.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationBenilov, E. S., Benilov, M. S., & O’Brien, S. B. G. (2009). Existence and stability of regularized shock solutions, with applications to rimming flows. Journal of Engineering Mathematics, 63(2), 197-212. DOI: 10.1007/s10665-008-9227-1pt_PT
dc.identifier.doi10.1007/s10665-008-9227-1pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.13/4532
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringerpt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectLiquid filmspt_PT
dc.subjectRimming flowspt_PT
dc.subjectShockspt_PT
dc.subjectStabilitypt_PT
dc.subjectSurface tensionpt_PT
dc.subject.pt_PT
dc.subjectFaculdade de Ciências Exatas e da Engenhariapt_PT
dc.titleExistence and stability of regularized shock solutions, with applications to rimming flowspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage212pt_PT
oaire.citation.issue2-4pt_PT
oaire.citation.startPage197pt_PT
oaire.citation.titleJournal of Engineering Mathematicspt_PT
oaire.citation.volume63pt_PT
person.familyNameBenilov
person.givenNameMikhail
person.identifier.ciencia-id0F14-A79A-97C1
person.identifier.orcid0000-0001-9059-1948
person.identifier.ridK-4443-2015
person.identifier.scopus-author-id7005138676
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication5ccf95a3-53d5-446c-857c-55d64b887175
relation.isAuthorOfPublication.latestForDiscovery5ccf95a3-53d5-446c-857c-55d64b887175

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