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Kelvin-Voigt equations with anisotropic diffusion, relaxation and damping: Blow-up and large time behavior

2021Journal article Restricted access
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dc.contributor.authorAntontsev, S.
dc.contributor.authorOliveira, H. B. de
dc.contributor.authorKhompysh, Kh
dc.date.accessioned2021-09-08T10:58:14Z
dc.date.available2021-09-08T10:58:14Z
dc.date.issued2021
dc.description.abstractA nonlinear initial and boundary-value problem for the Kelvin-Voigt equations with anisotropic diffusion, relaxation and absorption/damping terms is considered in this work. The global and local unique solvability of the problem was established in (J. Math. Anal. Appl. 473(2) (2019) 1122-1154). In the present work, we show how all the anisotropic exponents of nonlinearity and all anisotropic coefficients should interact with the problem data for the solutions of this problem display exponential and polynomial time-decays. We also establish the conditions for the solutions of this problem to blow-up in a finite time in three different cases: problem without convection, full anisotropic problem, and the problem with isotropic relaxation.
dc.description.sponsorshipRussian Science Foundation, RussiaRussian Science Foundation (RSF) [19-11-00069]; Portuguese Foundation for Science and Technology, PortugalPortuguese Foundation for Science and Technology [SFRH/BSAB/135242/2017]; FCT -Fundacao para a Ciencia e a TecnologiaPortuguese Foundation for Science and Technology [UIDB/04561/2020]; Ministry of Science and Education of the Republic of Kazakhstan (MES RK), Kazakhstan [AP08052425]
dc.description.versioninfo:eu-repo/semantics/publishedVersion
dc.identifier.doi10.3233/ASY-201597
dc.identifier.issn0921-7134
dc.identifier.urihttp://hdl.handle.net/10400.1/17067
dc.language.isoeng
dc.peerreviewedyes
dc.publisherIOS PRESS
dc.relationAnálise de modelos mais complexos da Mecânica dos Fluídos
dc.relationCenter for Mathematics, Fundamental Applications and Operations Research
dc.subjectKelvin-Voigt equations
dc.subjectAnisotropic diffusion
dc.subjectAnisotropic relaxation
dc.subjectAnisotropic damping
dc.subjectLarge time behavior
dc.subjectBlow-up
dc.subject.otherMathematics
dc.titleKelvin-Voigt equations with anisotropic diffusion, relaxation and damping: Blow-up and large time behavior
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleAnálise de modelos mais complexos da Mecânica dos Fluídos
oaire.awardTitleCenter for Mathematics, Fundamental Applications and Operations Research
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/OE/SFRH%2FBSAB%2F135242%2F2017/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04561%2F2020/PT
oaire.citation.endPage157
oaire.citation.issue2
oaire.citation.startPage125
oaire.citation.titleAsymptotic Analysis
oaire.citation.volume121
oaire.fundingStreamOE
oaire.fundingStream6817 - DCRRNI ID
person.familyNameBorges de Oliveira
person.givenNameHermenegildo
person.identifier.ciencia-id4A15-7156-6A00
person.identifier.orcid0000-0001-9053-8442
person.identifier.ridF-3186-2014
person.identifier.scopus-author-id7004475473
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsrestrictedAccess
rcaap.typearticle
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