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Homogenization of partial differential equations : from multiple scale expansions to Tartar's H-measures
Dissertation (MSc)--University of Pretoria, 2015.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2016
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| _version_ | 1867613607349452800 |
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| access_status_str | Open Access |
| author2 | Sango, Mamadou |
| author_browse | Sango, Mamadou |
| author_facet | Sango, Mamadou |
| collection | Thesis |
| dc_rights_str_mv | © 2016, 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, 2015. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/53488 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:50.049Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| 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:2263/53488 Homogenization of partial differential equations : from multiple scale expansions to Tartar's H-measures Sango, Mamadou chigoann2000@yahoo.com Emereuwa, Chigoziem A. UCTD Dissertation (MSc)--University of Pretoria, 2015. Homogenization theory has emerged over the last decades as a fundamental tool in the study of mathematical problems arising in processes taking place in highly heterogeneous media, such as composite materials, ow through porous medium, living tissues, just to cite a few. The main feature of these problems is the presence of multiple scales, notably microscopic and macroscopic scales. A prominent and simpli ed theory of homogenization is period homogenization based on assumptions of periodic structure in the problems investigated. Since its inception, several challenges had to be overcome in the evolution of the theory. My dissertation was aimed at covering these challenges and the corresponding deep methods that were invented subsequently. First, we study elliptic partial di erential equations with periodic coe cients using the multiscale expansion and Tartar's method of oscillating test functions. Then we discuss nonlinear homogenization using the div-curl lemma, compensated compactness, Young measures and H-measures. We shall endeavour to motivate the emergence of these methods along their historical flow. Mathematics and Applied Mathematics MSc Unrestricted 2016-07-01T10:32:53Z 2016-07-01T10:32:53Z 2016-04-13 2015 Dissertation Emereuwa, CA 2016, Homogenization of partial differential equations : from multiple scale expansions to Tartar's H-measures, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/53488> A2016 http://hdl.handle.net/2263/53488 en © 2016, 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 Homogenization of partial differential equations : from multiple scale expansions to Tartar's H-measures |
| title | Homogenization of partial differential equations : from multiple scale expansions to Tartar's H-measures |
| title_full | Homogenization of partial differential equations : from multiple scale expansions to Tartar's H-measures |
| title_fullStr | Homogenization of partial differential equations : from multiple scale expansions to Tartar's H-measures |
| title_full_unstemmed | Homogenization of partial differential equations : from multiple scale expansions to Tartar's H-measures |
| title_short | Homogenization of partial differential equations : from multiple scale expansions to Tartar's H-measures |
| title_sort | homogenization of partial differential equations from multiple scale expansions to tartar s h measures |
| topic | UCTD |
| url | http://hdl.handle.net/2263/53488 |