Publication:
Existence of an attractor and determining modes for structurally damped nonlinear wave equations

dc.contributor.departmentDepartment of Mathematics
dc.contributor.departmentGraduate School of Sciences and Engineering
dc.contributor.kuauthorBilgin, Bilgesu Arif
dc.contributor.kuauthorKalantarov, Varga
dc.contributor.kuprofilePhD Student
dc.contributor.kuprofileFaculty Member
dc.contributor.schoolcollegeinstituteGRADUATE SCHOOL OF SCIENCES AND ENGINEERING
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.contributor.yokidN/A
dc.contributor.yokid117655
dc.date.accessioned2024-11-10T00:02:12Z
dc.date.issued2018
dc.description.abstractThe paper is devoted to the study of asymptotic behavior as t -> +infinity of solutions of initial boundary value problem for structurally damped semi-linear wave equation partial derivative(2)(t)u(x, t) - Delta u(x, t)+gamma(-Delta)(theta)partial derivative(t) u(x,t) + f(u) = g(x), theta is an element of(0, 1), x is an element of Omega, t > 0 under homogeneous Dirichlet's boundary condition in a bounded domain Omega subset of R-3. We proved that the asymptotic behavior as t -> infinity of solutions of this problem is completely determined by dynamics of the first N Fourier modes, when N is large enough. We also proved that the semigroup generated by this problem when theta is an element of(1/2, 1) possesses an exponential attractor. (C) 2017 Elsevier B.V. All rights reserved.
dc.description.indexedbyWoS
dc.description.indexedbyScopus
dc.description.openaccessNO
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.volume376
dc.identifier.doi10.1016/j.physd.2017.12.001
dc.identifier.eissn1872-8022
dc.identifier.issn0167-2789
dc.identifier.quartileQ1
dc.identifier.scopus2-s2.0-85039740519
dc.identifier.urihttp://dx.doi.org/10.1016/j.physd.2017.12.001
dc.identifier.urihttps://hdl.handle.net/20.500.14288/16096
dc.identifier.wos437962900003
dc.keywordsStrongly damped wave equations
dc.keywordsNonlinear wave equation
dc.keywordsStructurally damped wave equation
dc.keywordsDetermining modes
dc.keywordsGlobal solution
dc.keywordsGlobal attractor
dc.languageEnglish
dc.publisherElsevier Science Bv
dc.sourcePhysica D-Nonlinear Phenomena
dc.subjectMathematics
dc.subjectApplied mathematics
dc.subjectPhysics
dc.subjectFluids
dc.subjectPlasmas
dc.subjectPhysics
dc.subjectMathematical
dc.titleExistence of an attractor and determining modes for structurally damped nonlinear wave equations
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.authorid0000-0002-6282-4027
local.contributor.authorid0000-0003-0928-3513
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
relation.isOrgUnitOfPublication2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isOrgUnitOfPublication3fc31c89-e803-4eb1-af6b-6258bc42c3d8
relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isParentOrgUnitOfPublication434c9663-2b11-4e66-9399-c863e2ebae43
relation.isParentOrgUnitOfPublicationaf0395b0-7219-4165-a909-7016fa30932d
relation.isParentOrgUnitOfPublication.latestForDiscoveryaf0395b0-7219-4165-a909-7016fa30932d

Files