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Analysis and numerical approximations of exact controllability problems for systems governed by parabolic differential equations

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dc.contributor.authorCao, Yanzhaoen
dc.contributor.committeechairGunzburger, Max D.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberLin, Taoen
dc.contributor.committeememberPeterson, Janet S.en
dc.contributor.committeememberRogers, Robert C.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:10:56Zen
dc.date.adate2006-05-11en
dc.date.available2014-03-14T21:10:56Zen
dc.date.issued1996-06-16en
dc.date.rdate2006-05-11en
dc.date.sdate2006-05-11en
dc.description.abstractThe exact controllability problems for systems modeled by linear parabolic differential equations and the Burger's equations are considered. A condition on the exact controllability of linear parabolic equations is obtained using the optimal control approach. We also prove that the exact control is the limit of appropriate optimal controls. A numerical scheme of computing exact controls for linear parabolic equations is constructed based on this result. To obtain numerical approximation of the exact control for the Burger's equation, we first construct another numerical scheme of computing exact controls for linear parabolic equations by reducing the problem to a hypoelliptic equation problem. A numerical scheme for the exact zero control of the Burger's equation is then constructed, based on the simple iteration of the corresponding linearized problem. The efficiency of the computational methods are illustrated by a variety of numerical experiments.en
dc.description.degreePh. D.en
dc.format.extentviii, 83 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-05112006-154821en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05112006-154821/en
dc.identifier.urihttp://hdl.handle.net/10919/37771en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1996.C36.pdfen
dc.relation.isformatofOCLC# 35286138en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectoptimal control approachen
dc.subject.lccLD5655.V856 1996.C36en
dc.titleAnalysis and numerical approximations of exact controllability problems for systems governed by parabolic differential equationsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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