Ondas viajantes para um problema de EDP Parabólico
| Ano de defesa: | 2016 |
|---|---|
| Autor(a) principal: | |
| Orientador(a): |
Mota, Jesus Carlos da
 |
| Banca de defesa: |
Mota, Jesus Carlos da
, , |
| Tipo de documento: | Dissertação |
| Tipo de acesso: | Acesso aberto |
| Idioma: | por |
| Instituição de defesa: |
Universidade Federal de Goiás
|
| Programa de Pós-Graduação: |
Programa de Pós-graduação em Matemática (IME)
|
| Departamento: |
Instituto de Matemática e Estatística - IME (RG)
|
| País: |
Brasil
|
| Palavras-chave em Português: | |
| Palavras-chave em Inglês: | |
| Área do conhecimento CNPq: | |
| Link de acesso: | http://repositorio.bc.ufg.br/tede/handle/tede/6138 |
Resumo: | In this work we study and show the existence of traveling waves solutions for a system of parabolic partial differential equations (PPDE’s) which model in-situ combustion process in porous medium. The in-situ combustion process is a thermal method to recovery oil from petrolific reservoirs. The system deduction is making considering two layers of porous rock and aplying the physical laws of balance energy, fuel mass, oxygen mass, total gas mass, and the Darcy’s law which link the pressure and volumetric flow rate. The traveling waves are obtained making an useful variavel change such that convert the PPDE’s system in an ordinary differential equations system (ODE’s) where the existence of heteroclinic orbits is equivalent to the existence of a traveling waves for the system of PPDE’s which connect the burned state to the unburned state. In the proof of the existence and uniquess of such orbits are used basic tools in Qualitative Ordinary Differential Equations Theory, Dynamical Systems, Perturbation Theory and TravelingWaves Theory with special mention to Singular Perturbation Theory and Melnikov Method inside of the perturbation theory. |
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Mota, Jesus Carlos dahttp://lattes.cnpq.br/8457974658695539Mota, Jesus Carlos dahttp://lattes.cnpq.br/8457974658695539Medrado, João Carlos da RochaSouza, Aparecido Jesuino deGarzon, Brayan Mauricio Rodriguez2016-09-08T17:05:21Z2016-03-04GARZON, Brayan Mauricio Rodriguez. Ondas viajantes para um problema de EDP Parabólico. 2016. 79 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2016.http://repositorio.bc.ufg.br/tede/handle/tede/6138In this work we study and show the existence of traveling waves solutions for a system of parabolic partial differential equations (PPDE’s) which model in-situ combustion process in porous medium. The in-situ combustion process is a thermal method to recovery oil from petrolific reservoirs. The system deduction is making considering two layers of porous rock and aplying the physical laws of balance energy, fuel mass, oxygen mass, total gas mass, and the Darcy’s law which link the pressure and volumetric flow rate. The traveling waves are obtained making an useful variavel change such that convert the PPDE’s system in an ordinary differential equations system (ODE’s) where the existence of heteroclinic orbits is equivalent to the existence of a traveling waves for the system of PPDE’s which connect the burned state to the unburned state. In the proof of the existence and uniquess of such orbits are used basic tools in Qualitative Ordinary Differential Equations Theory, Dynamical Systems, Perturbation Theory and TravelingWaves Theory with special mention to Singular Perturbation Theory and Melnikov Method inside of the perturbation theory.Neste trabalho estudamos e mostramos a existência de soluções do tipo onda viajante para um sistema de equações diferenciais parciais parabólico (EDPP’s) que modela um processo de combustão in-situ através de um meio poroso. A combustão in-situ é um método térmico de recuperação de óleo de reservatórios petrolíferos. O sistema é deduzido considerando duas camadas de rocha porosa e aplicando as leis físicas de balanço de energia, de massa de combustível, oxigênio, gás total, e a lei de Darcy que relaciona a pressão e a vazão volumétrica dos fluidos considerados. As ondas viajantes são obtidas fazendo uma mudança de variáveis apropriada de modo que o sistema de EDPP’s se transforme num sistema de equações diferenciais ordinárias (EDO’s), onde a existência de uma orbita conectando dois equilíbrios corresponde-se com a existência de uma onda viajante do sistema de EDPP’s, conectando um estado totalmente queimado com um estado não queimado. Para a prova de existência e unicidade das referidas órbitas são utilizadas ferramentas básicas da Teoria qualitativa das Equações Diferenciais Ordinárias, Sistemas Dinâmicos, Teoria da Perturbação e Teoria de Ondas Viajantes, ressaltando dentro da teoria da perturbação a técnica da Perturbação Singular Geométrica e o Método de Melnikov.Submitted by Jaqueline Silva (jtas29@gmail.com) on 2016-09-08T17:05:05Z No. of bitstreams: 2 Dissertação - Brayan Maurício Rodrigues Garzon - 2016.pdf: 1077822 bytes, checksum: 22f0f3e54ede997e3bbec84f88406474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2016-09-08T17:05:21Z (GMT) No. of bitstreams: 2 Dissertação - Brayan Maurício Rodrigues Garzon - 2016.pdf: 1077822 bytes, checksum: 22f0f3e54ede997e3bbec84f88406474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2016-09-08T17:05:21Z (GMT). No. of bitstreams: 2 Dissertação - Brayan Maurício Rodrigues Garzon - 2016.pdf: 1077822 bytes, checksum: 22f0f3e54ede997e3bbec84f88406474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-04Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessCombustãoIn-situMeio porosoMétodo melnikovPerturbação singularCombustionIn-situMelnikov methodPorous mediumTraveling wavesSingular perturbationCIENCIAS EXATAS E DA TERRA::MATEMATICAOndas viajantes para um problema de EDP ParabólicoTravelling waves for a parabolic PDE probleminfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis6600717948137941247600600600600-4268777512335152015-70908234179844016942075167498588264571reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; 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| dc.title.por.fl_str_mv |
Ondas viajantes para um problema de EDP Parabólico |
| dc.title.alternative.eng.fl_str_mv |
Travelling waves for a parabolic PDE problem |
| title |
Ondas viajantes para um problema de EDP Parabólico |
| spellingShingle |
Ondas viajantes para um problema de EDP Parabólico Garzon, Brayan Mauricio Rodriguez Combustão In-situ Meio poroso Método melnikov Perturbação singular Combustion In-situ Melnikov method Porous medium Traveling waves Singular perturbation CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| title_short |
Ondas viajantes para um problema de EDP Parabólico |
| title_full |
Ondas viajantes para um problema de EDP Parabólico |
| title_fullStr |
Ondas viajantes para um problema de EDP Parabólico |
| title_full_unstemmed |
Ondas viajantes para um problema de EDP Parabólico |
| title_sort |
Ondas viajantes para um problema de EDP Parabólico |
| author |
Garzon, Brayan Mauricio Rodriguez |
| author_facet |
Garzon, Brayan Mauricio Rodriguez |
| author_role |
author |
| dc.contributor.advisor1.fl_str_mv |
Mota, Jesus Carlos da |
| dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8457974658695539 |
| dc.contributor.referee1.fl_str_mv |
Mota, Jesus Carlos da |
| dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/8457974658695539 |
| dc.contributor.referee2.fl_str_mv |
Medrado, João Carlos da Rocha |
| dc.contributor.referee3.fl_str_mv |
Souza, Aparecido Jesuino de |
| dc.contributor.author.fl_str_mv |
Garzon, Brayan Mauricio Rodriguez |
| contributor_str_mv |
Mota, Jesus Carlos da Mota, Jesus Carlos da Medrado, João Carlos da Rocha Souza, Aparecido Jesuino de |
| dc.subject.por.fl_str_mv |
Combustão In-situ Meio poroso Método melnikov Perturbação singular |
| topic |
Combustão In-situ Meio poroso Método melnikov Perturbação singular Combustion In-situ Melnikov method Porous medium Traveling waves Singular perturbation CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| dc.subject.eng.fl_str_mv |
Combustion In-situ Melnikov method Porous medium Traveling waves Singular perturbation |
| dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| description |
In this work we study and show the existence of traveling waves solutions for a system of parabolic partial differential equations (PPDE’s) which model in-situ combustion process in porous medium. The in-situ combustion process is a thermal method to recovery oil from petrolific reservoirs. The system deduction is making considering two layers of porous rock and aplying the physical laws of balance energy, fuel mass, oxygen mass, total gas mass, and the Darcy’s law which link the pressure and volumetric flow rate. The traveling waves are obtained making an useful variavel change such that convert the PPDE’s system in an ordinary differential equations system (ODE’s) where the existence of heteroclinic orbits is equivalent to the existence of a traveling waves for the system of PPDE’s which connect the burned state to the unburned state. In the proof of the existence and uniquess of such orbits are used basic tools in Qualitative Ordinary Differential Equations Theory, Dynamical Systems, Perturbation Theory and TravelingWaves Theory with special mention to Singular Perturbation Theory and Melnikov Method inside of the perturbation theory. |
| publishDate |
2016 |
| dc.date.accessioned.fl_str_mv |
2016-09-08T17:05:21Z |
| dc.date.issued.fl_str_mv |
2016-03-04 |
| dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/masterThesis |
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masterThesis |
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publishedVersion |
| dc.identifier.citation.fl_str_mv |
GARZON, Brayan Mauricio Rodriguez. Ondas viajantes para um problema de EDP Parabólico. 2016. 79 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2016. |
| dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/6138 |
| identifier_str_mv |
GARZON, Brayan Mauricio Rodriguez. Ondas viajantes para um problema de EDP Parabólico. 2016. 79 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2016. |
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http://repositorio.bc.ufg.br/tede/handle/tede/6138 |
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por |
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por |
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