Formation of shocks in higher-order nonlinear dispersion PDEs: nonuniqueness and nonexistence of entropy

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dc.creatorGalaktionov, V. A.
dc.date2009-02-10
dc.date.accessioned2026-07-07T12:39:52Z
dc.date.available2026-07-07T12:39:52Z
dc.descriptionIt is shown that third-order 1D nonlinear dispersion equations admit single point gradient catastrophe, described by blow-up-type similarity solutions. After blow-up, the solutions admit shock wave-type self-similar extensions. Snce such extensions are not unique, this implies the principle nonuniqueness of shock-type solutions and also nonexistence of any entropy-type description of proper unique solutions. A difficult free-boundary setting, with extra conditions specified on shocks, are necessary to restore uniqueness in such problems.
dc.description19 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/0902.1635
dc.identifierhttp://arxiv.org/abs/0902.1635
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219269
dc.subjectAnalysis of PDEs
dc.subject35K55, 35K40, 35K65
dc.titleFormation of shocks in higher-order nonlinear dispersion PDEs: nonuniqueness and nonexistence of entropy
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