Global existence in L1 for the square-well kinetic equation

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dc.contributor.authorLiu, Rongshengen
dc.contributor.committeechairGreenberg, Williamen
dc.contributor.committeememberZweifel, Paul F.en
dc.contributor.committeememberHagedorn, George A.en
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberBeattie, Christopher A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:22:02Zen
dc.date.adate2005-10-24en
dc.date.available2014-03-14T21:22:02Zen
dc.date.issued1993-04-04en
dc.date.rdate2005-10-24en
dc.date.sdate2005-10-24en
dc.description.abstractAn attractive square-well is incorporated into the Enskog equation, in order to model the kinetic theory of a moderately dense gas with intermolecular potential. The existence of solutions to the Cauchy problem in <i>L</i>ยน. global in time and for arbitrary initial data. is proved. A simple derivation of the square-well kinetic equation is given. Lewis's method is used~ which starts from the Liouville equation of statistical mechanics. Then various symmetries of the collisional integrals are established. An H-theorem for entropy, mass, and momentum conservation is obtained, as well as an energy estimate, and key gain-loss estimates. Approximate equations for the square-well kinetic equation are constructed that preserve symmetries of the collisional integral. Existence of nonnegative solutions of the approximate equations and weak compactness are obtained. The velocity averaging lemma of Golse is then a principal tool in demonstrating the convergence of the approximate solutions to a solution of the renormalized square well kinetic equation. The existence of weak solution of the initial value problem for the square well kinetic equation is thus proved.en
dc.description.degreePh. D.en
dc.format.extentv, 85 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-10242005-124058en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10242005-124058/en
dc.identifier.urihttp://hdl.handle.net/10919/40106en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1993.L579.pdfen
dc.relation.isformatofOCLC# 29323480en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1993.L579en
dc.subject.lcshKinetic theory of gases -- Mathematical modelsen
dc.titleGlobal existence in L1 for the square-well kinetic equationen
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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