Gradient blow-up for a fourth-order quasilinear Boussinesq-type equation

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Show simple item record Álvarez Caudevilla, Pablo Evans, Jonathan Galaktionov, Victor A. 2021-04-13T09:53:29Z 2021-04-13T09:53:29Z 2018-08
dc.identifier.bibliographicCitation Álvarez-Caudevilla, P., D. Evans, J. & A. Galaktionov, V. (2018). Gradient blow-up for a fourth-order quasilinear Boussinesq-type equation. Discrete & Continuous Dynamical Systems, 38(8), pp. 3913–3938.
dc.identifier.issn 1078-0947
dc.description.abstract The Cauchy problem for a fourth-order Boussinesq-type quasilinear wave equation (QWE-4) of the form u(tt) = -(vertical bar u vertical bar(n) u)(xxxx) in R x R+, with a fixed exponent n > 0, and bounded smooth initial data, is considered. Self-similar single-point gradient blow-up solutions are studied. It is shown that such singular solutions exist and satisfy the case of the so-called self-similarity of the second type. Together with an essential and, often, key use of numerical methods to describe possible types of gradient blow-up, a "homotopy" approach is applied that traces out the behaviour of such singularity patterns as n -> 0(+), when the classic linear beam equation occurs u(tt) = - u(xxxx), with simple, better-known and understandable evolution properties.
dc.format.extent 26
dc.language.iso eng
dc.publisher American Institute of Mathematical Sciences (AIMS)
dc.rights © 2018 American Institute of Mathematical Sciences
dc.subject.other Fourth-order quasilinear wave equation
dc.subject.other Gradient blow-up
dc.subject.other Self- similarity of the second kind
dc.title Gradient blow-up for a fourth-order quasilinear Boussinesq-type equation
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. RYC-2014-15284
dc.relation.projectID Gobierno de España. MTM2016-80618-P
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 3913
dc.identifier.publicationissue 8
dc.identifier.publicationlastpage 3938
dc.identifier.publicationtitle Discrete & Continuous Dynamical Systems
dc.identifier.publicationvolume 38
dc.identifier.uxxi AR/0000022080
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.affiliation.dpto UC3M. Departamento de Matemáticas
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