Solution of conservation laws via convergence space completion

dc.contributor.advisorVan der Walt, Jan Harmen
dc.contributor.advisorAnguelov, Roumenen
dc.contributor.emaildfagbebaku@gmail.comen
dc.contributor.postgraduateAgbebaku, Dennis Ferdinand
dc.date.accessioned2013-09-07T12:19:49Z
dc.date.available2012-05-16en
dc.date.available2013-09-07T12:19:49Z
dc.date.created2012-04-13en
dc.date.issued2011en
dc.date.submitted2012-02-09en
dc.descriptionDissertation (MSc)--University of Pretoria, 2011.en
dc.description.abstractIt is well known that a classical solution of the initial value problem for a scalar conservation law may fail to exist on the whole domain of definition of the problem. For this reason, suitable generalized solutions of such problems, known as weak solutions, have been considered and studied extensively. However, weak solutions are not unique. In order to obtain a unique solution that is physically relevant, the vanishing viscosity method, amongst others, has been employed to single out a unique solution known as the entropy solution. In this thesis we present an alternative approach to the study of the entropy solution of conservation laws. The main novelty of our approach is that the theory of entropy solution of conservation law is presented in an operator theoretic setting. In this regard, the Order Completion Method for nonlinear PDEs, in the context of convergence vector spaces, is modified to obtain an operator equation which generalizes the initial value problem. This equation admits at most one solution, which may be represented as a Hausdorff continuous function. As a particular case, we apply our method to obtain the entropy solution of the Burger's equation. Copyrighten
dc.description.availabilityUnrestricteden
dc.description.departmentMathematics and Applied Mathematicsen
dc.identifier.citationAgbebaku, DF 2011, Solution of conservation laws via convergence space completion, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/27791 >en
dc.identifier.otherC12/4/110/gmen
dc.identifier.upetdurlhttp://upetd.up.ac.za/thesis/available/etd-02092012-103827/en
dc.identifier.urihttp://hdl.handle.net/2263/27791
dc.language.isoen
dc.publisherUniversity of Pretoriaen_ZA
dc.rights© 2011, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoriaen
dc.subjectConservation lawsen
dc.subjectEntropy solutionen
dc.subjectOrder completionen
dc.subjectConvergence spaceen
dc.subjectWyler completionen
dc.subjectHausdorff continuous function.en
dc.subjectUCTDen_US
dc.titleSolution of conservation laws via convergence space completionen
dc.typeDissertationen

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