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

Simple item page
dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.contributor.authorÁlvarez Caudevilla, Pablo
dc.contributor.authorEvans, Jonathan
dc.contributor.authorGalaktionov, Victor A.
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-04-13T09:53:29Z
dc.date.available2021-04-13T09:53:29Z
dc.date.issued2018-08
dc.description.abstractThe 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.extent26
dc.identifier.bibliographicCitationÁlvarez-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.doihttps://doi.org/10.3934/dcds.2018170
dc.identifier.issn1078-0947
dc.identifier.publicationfirstpage3913
dc.identifier.publicationissue8
dc.identifier.publicationlastpage3938
dc.identifier.publicationtitleDiscrete & Continuous Dynamical Systemsen
dc.identifier.publicationvolume38
dc.identifier.urihttps://hdl.handle.net/10016/32342
dc.identifier.uxxiAR/0000022080
dc.language.isoeng
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.relation.projectIDGobierno de España. RYC-2014-15284es
dc.relation.projectIDGobierno de España. MTM2016-80618-Pes
dc.rights© 2018 American Institute of Mathematical Sciencesen
dc.rights.accessRightsopen accessen
dc.subject.ecienciaMatemáticases
dc.subject.otherFourth-order quasilinear wave equationen
dc.subject.otherGradient blow-upen
dc.subject.otherSelf- similarity of the second kinden
dc.titleGradient blow-up for a fourth-order quasilinear Boussinesq-type equationen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Gradient_DCDSA_2018_ps.pdf
Size:
915.02 KB
Format:
Adobe Portable Document Format
Download
Collections
DM - Artículos de Revistas