Publication: Gradient blow-up for a fourth-order quasilinear Boussinesq-type equation
dc.affiliation.dpto | UC3M. Departamento de Matemáticas | es |
dc.contributor.author | Álvarez Caudevilla, Pablo | |
dc.contributor.author | Evans, Jonathan | |
dc.contributor.author | Galaktionov, Victor A. | |
dc.contributor.funder | Ministerio de Economía y Competitividad (España) | es |
dc.date.accessioned | 2021-04-13T09:53:29Z | |
dc.date.available | 2021-04-13T09:53:29Z | |
dc.date.issued | 2018-08 | |
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. | en |
dc.format.extent | 26 | |
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. | en |
dc.identifier.doi | https://doi.org/10.3934/dcds.2018170 | |
dc.identifier.issn | 1078-0947 | |
dc.identifier.publicationfirstpage | 3913 | |
dc.identifier.publicationissue | 8 | |
dc.identifier.publicationlastpage | 3938 | |
dc.identifier.publicationtitle | Discrete & Continuous Dynamical Systems | en |
dc.identifier.publicationvolume | 38 | |
dc.identifier.uri | https://hdl.handle.net/10016/32342 | |
dc.identifier.uxxi | AR/0000022080 | |
dc.language.iso | eng | |
dc.publisher | American Institute of Mathematical Sciences (AIMS) | en |
dc.relation.projectID | Gobierno de España. RYC-2014-15284 | es |
dc.relation.projectID | Gobierno de España. MTM2016-80618-P | es |
dc.rights | © 2018 American Institute of Mathematical Sciences | en |
dc.rights.accessRights | open access | en |
dc.subject.eciencia | Matemáticas | es |
dc.subject.other | Fourth-order quasilinear wave equation | en |
dc.subject.other | Gradient blow-up | en |
dc.subject.other | Self- similarity of the second kind | en |
dc.title | Gradient blow-up for a fourth-order quasilinear Boussinesq-type equation | en |
dc.type | research article | * |
dc.type.hasVersion | AM | * |
dspace.entity.type | Publication |
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