Vlasov-Fokker-Planck type kinetic models for multilane traffic flow and large time behavior of kinetic density by entropy methods

dc.contributor.authorZhou, Ting
dc.contributor.supervisorIllner, Reinhard
dc.date.accessioned2010-01-25T16:50:09Z
dc.date.available2010-01-25T16:50:09Z
dc.date.copyright2006en
dc.date.issued2010-01-25T16:50:09Z
dc.degree.departmentDept. of Mathematics and Statisticsen
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractWe present a class of multi-lane traffic models of Vlasov-Fokker-Planck type incorporating non-local and time-delayed braking/acceleration, diffu¬sion and lane changing terms whose dependencies are based on empirical guidelines. By investigating the spatially homogeneous case with non-zero passing probability incorporated in the braking term. we are left with the drift diffusion equation. which leads to a multi-valued fundamental diagram. As a novelty of this thesis. we find out that the monotonicity of the quotient between the braking/acceleration and the diffusion term in average speed guarantees the single-valued fundamental diagram. We study the large time behavior of the time-dependent kinetic density by convex entropy methods based on [3]. With a positive "residual" diffusion, convergence results remain with fewer assumptions. Two simplified examples are studied to illustrate the application of entropy methods.en
dc.identifier.urihttp://hdl.handle.net/1828/2098
dc.languageEnglisheng
dc.language.isoenen
dc.rightsAvailable to the World Wide Weben
dc.subjecttraffic flowen
dc.subjectmathematical modelsen
dc.subject.lcshUVic Subject Index::Sciences and Engineering::Mathematicsen
dc.titleVlasov-Fokker-Planck type kinetic models for multilane traffic flow and large time behavior of kinetic density by entropy methodsen
dc.typeThesisen

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