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Stability of lie groups of nonlinear hyperbolic equations
Thesis (PhD)--University of Pretoria, 1997.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2022
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| _version_ | 1867613595737522176 |
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| access_status_str | Open Access |
| author2 | Rosinger, Elemer E. |
| author_browse | Rosinger, Elemer E. |
| author_facet | Rosinger, Elemer E. |
| collection | Thesis |
| dc_rights_str_mv | © 2020 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 | Thesis (PhD)--University of Pretoria, 1997. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/85368 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:39.160Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| 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:2263/85368 Stability of lie groups of nonlinear hyperbolic equations Rosinger, Elemer E. Omolo-Ongati, Naftali UCTD Stability lie groups nonlinear hyperbolic equations Thesis (PhD)--University of Pretoria, 1997. In this thesis the stability of the Lie group invariance of classical solutions of large classes of nonlinear partial differential equations is studied. We give a theoretical framework for the construction of approximate groups for nonlinear partial differential equations. In particular, stability symmetries for the perturbed nonlinear wave equation սtt+ eut = (ƒ (x, u) ux]x are presented here for the first time. This research is a particularly important stability study, since it applies to large classes of - earlier unknown - classical solutions of nonlinear partial differential equations as well as to their symmetries. These equations and solutions model, amongst others, important laws of nature. Chapter 1 is devoted to the general concepts of Lie group theory. A detailed account is given of the applications of Lie groups to both ordinary and partial differential equations. To date the only known method of obtaining particular solutions to complicated systems of differential equations is by Lie group symmetry analysis. This is now well known in the literature. The Lie group symmetry analysis, however, has some limitations. Any small perturbation of an equation disturbs the group admitted by it and this reduces the practical value of group theoretic methods in general. The theory of stability analysis presented in chapter 2 overcomes this problem. This technique, originated by N .Kh. Ibragimov around 1988, generates groups that are stable under small, or even classes of more arbitrary, perturbations of the differential equations involved. The exact Lie groups admitted by the nonlinear wave equation սtt = (ƒ (x, u) ux]x and the corresponding perturbed equation are discussed in chapter 3. Finally, in chapter 4, the construction of stability groups admitted by the perturbed nonlinear wave equation are set out in detail. Mathematics and Applied Mathematics PhD Unrestricted 2022-05-17T11:20:30Z 2022-05-17T11:20:30Z 2021/11/02 1997 Thesis * https://repository.up.ac.za/handle/2263/85368 en © 2020 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 | UCTD Stability lie groups nonlinear hyperbolic equations Stability of lie groups of nonlinear hyperbolic equations |
| title | Stability of lie groups of nonlinear hyperbolic equations |
| title_full | Stability of lie groups of nonlinear hyperbolic equations |
| title_fullStr | Stability of lie groups of nonlinear hyperbolic equations |
| title_full_unstemmed | Stability of lie groups of nonlinear hyperbolic equations |
| title_short | Stability of lie groups of nonlinear hyperbolic equations |
| title_sort | stability of lie groups of nonlinear hyperbolic equations |
| topic | UCTD Stability lie groups nonlinear hyperbolic equations |
| url | https://repository.up.ac.za/handle/2263/85368 |