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Non-existence of global solutions to nonlinear wave equations with positive initial energy

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dc.contributor.departmentDepartment of Mathematics
dc.contributor.departmentGraduate School of Sciences and Engineering
dc.contributor.kuauthorPhD Student, Bilgin, Bilgesu Arif
dc.contributor.kuauthorFaculty Member, Kalantarov, Varga
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.contributor.schoolcollegeinstituteGRADUATE SCHOOL OF SCIENCES AND ENGINEERING
dc.date.accessioned2024-11-09T23:51:43Z
dc.date.issued2018
dc.description.abstractWe consider the Cauchy problem for nonlinear abstract wave equations in a Hilbert space. Our main goal is to show that this problem has solutions with arbitrary positive initial energy that blow up in a finite time. The main theorem is proved by employing a result on growth of solutions of abstract nonlinear wave equation and the concavity method. A number of examples of nonlinear wave equations are given. A result on blow up of solutions with arbitrary positive initial energy to the initial boundary value problem for the wave equation under nonlinear boundary conditions is also obtained.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue3
dc.description.openaccessYES
dc.description.sponsoredbyTubitakEuN/A
dc.description.volume17
dc.identifier.doi10.3934/cpaa.2018048
dc.identifier.eissn1553-5258
dc.identifier.issn1534-0392
dc.identifier.scopus2-s2.0-85044411854
dc.identifier.urihttps://doi.org/10.3934/cpaa.2018048
dc.identifier.urihttps://hdl.handle.net/20.500.14288/14761
dc.identifier.wos439236400011
dc.keywordsGlobal non-existence
dc.keywordsBlow up
dc.keywordsDifferential operator equation
dc.keywordsConcavity method
dc.keywordsPositive energy
dc.keywordsKlein-gordon equations
dc.keywordsTime blow-up
dc.keywordsCauchy-problem
dc.keywordsHyperbolic-equations
dc.keywordsBoundary-conditions
dc.keywordsExistence
dc.keywordsInstability
dc.keywordsTheorems
dc.keywordsSystem
dc.language.isoeng
dc.publisherAmer Inst Mathematical Sciences-Aims
dc.relation.ispartofCommunications On Pure And Applied Analysis
dc.subjectMathematics
dc.subjectApplied mathematics
dc.titleNon-existence of global solutions to nonlinear wave equations with positive initial energy
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorBilgin, Bilgesu Arif
local.contributor.kuauthorKalantarov, Varga
local.publication.orgunit1GRADUATE SCHOOL OF SCIENCES AND ENGINEERING
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
local.publication.orgunit2Graduate School of Sciences and Engineering
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