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Solution of conservation laws via convergence space completion
Dissertation (MSc)--University of Pretoria, 2011.
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| Format: | Thesis |
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University of Pretoria
2013
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| _version_ | 1867613448065515520 |
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| access_status_str | Open Access |
| author2 | Van der Walt, Jan Harm |
| author_browse | Van der Walt, Jan Harm |
| author_facet | Van der Walt, Jan Harm |
| collection | Thesis |
| dc_rights_str_mv | © 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 Pretoria |
| description | Dissertation (MSc)--University of Pretoria, 2011. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/27791 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:36:18.085Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/27791 Solution of conservation laws via convergence space completion Van der Walt, Jan Harm Anguelov, Roumen dfagbebaku@gmail.com Agbebaku, Dennis Ferdinand Conservation laws Entropy solution Order completion Convergence space Wyler completion Hausdorff continuous function. UCTD Dissertation (MSc)--University of Pretoria, 2011. It 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. Copyright Mathematics and Applied Mathematics Unrestricted 2013-09-07T12:19:49Z 2012-05-16 2013-09-07T12:19:49Z 2012-04-13 2011 2012-02-09 Dissertation Agbebaku, DF 2011, Solution of conservation laws via convergence space completion, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/27791 > C12/4/110/gm http://hdl.handle.net/2263/27791 http://upetd.up.ac.za/thesis/available/etd-02092012-103827/ © 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 Pretoria application/pdf University of Pretoria |
| spellingShingle | Conservation laws Entropy solution Order completion Convergence space Wyler completion Hausdorff continuous function. UCTD Solution of conservation laws via convergence space completion |
| title | Solution of conservation laws via convergence space completion |
| title_full | Solution of conservation laws via convergence space completion |
| title_fullStr | Solution of conservation laws via convergence space completion |
| title_full_unstemmed | Solution of conservation laws via convergence space completion |
| title_short | Solution of conservation laws via convergence space completion |
| title_sort | solution of conservation laws via convergence space completion |
| topic | Conservation laws Entropy solution Order completion Convergence space Wyler completion Hausdorff continuous function. UCTD |
| url | http://hdl.handle.net/2263/27791 http://upetd.up.ac.za/thesis/available/etd-02092012-103827/ |