Uniqueness of global weak solution for some hyperbolic conservation system

Abstract. In the present work, we study the uniqueness of entropy solutions for the Riemann and Cauchy problems associated to the Suliciu relaxation system where the initial data satisfies the conditions H1 and H2. Moreover, the solution is in L∞ space. Also, we show the explixit solutions for the C...

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Autores:
De la Cruz Guerrero, Richard Alexander
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2014
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/51990
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/51990
http://bdigital.unal.edu.co/46238/
Palabra clave:
51 Matemáticas / Mathematics
Uniqueness
Suliciu relaxation system
Cauchy and Riemann problems
Global weak solutions
Delta shock solutions
Unicidad
Sistema de relajación de Suliciu
Problemas de Cauchy y Riemann
Soluciones débiles globales
Soluciones delta choques
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_50b46d279818553ecb45f56bb62095ec
oai_identifier_str oai:repositorio.unal.edu.co:unal/51990
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Rendón Arbeláez, LeonardoDe la Cruz Guerrero, Richard Alexander94bacb5a-141f-48a4-b3f1-1cb41613bbe83002019-06-29T13:15:31Z2019-06-29T13:15:31Z2014https://repositorio.unal.edu.co/handle/unal/51990http://bdigital.unal.edu.co/46238/Abstract. In the present work, we study the uniqueness of entropy solutions for the Riemann and Cauchy problems associated to the Suliciu relaxation system where the initial data satisfies the conditions H1 and H2. Moreover, the solution is in L∞ space. Also, we show the explixit solutions for the Cauchy problem and generalized Riemann problem. When the condition H1 is not satisfied delta shock solutions are obtained for the Riemann problem associated to the Suliciu relaxation system. To guarantee uniqueness of delta shock solutions, we employ a generalization of the Rankine-Hugoniot condition together with a suitable entropy condition.Resumen. En el presente trabajo se estudia la unicidad de soluciones entrópicas para los problemas de Riemann y Cauchy asociados al sistema de relajación de Suliciu donde el dato inicial satisface las condiciones H1 y H2. Además, la solución se encuentran en el espacio L∞. También, se muestra las soluciones explícitas para el problema de Cauchy y el problema generalizado de Riemann. Cuando la condición H1 no se satisface, soluciones delta choques solution son obtenidas para el problema de Riemann asociado al sistema de relajación de Suliciu. Para garantizar unicidad de soluciones delta choques, se emplea una generalización de la condición de Rankine-Hugoniot junto con una condición de entropía adecuada.Doctoradoapplication/pdfspaUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de MatemáticasDepartamento de MatemáticasDe la Cruz Guerrero, Richard Alexander (2014) Uniqueness of global weak solution for some hyperbolic conservation system. Doctorado thesis, Universidad Nacional de Colombia.51 Matemáticas / MathematicsUniquenessSuliciu relaxation systemCauchy and Riemann problemsGlobal weak solutionsDelta shock solutionsUnicidadSistema de relajación de SuliciuProblemas de Cauchy y RiemannSoluciones débiles globalesSoluciones delta choquesUniqueness of global weak solution for some hyperbolic conservation systemTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDORIGINAL01830415.2014.pdfapplication/pdf468994https://repositorio.unal.edu.co/bitstream/unal/51990/1/01830415.2014.pdf05aca93499d22179a3a50afbf17b8d3fMD51THUMBNAIL01830415.2014.pdf.jpg01830415.2014.pdf.jpgGenerated Thumbnailimage/jpeg4413https://repositorio.unal.edu.co/bitstream/unal/51990/2/01830415.2014.pdf.jpg5b0d26a739c77552e8e642af51af0fbeMD52unal/51990oai:repositorio.unal.edu.co:unal/519902024-02-28 23:09:57.58Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Uniqueness of global weak solution for some hyperbolic conservation system
title Uniqueness of global weak solution for some hyperbolic conservation system
spellingShingle Uniqueness of global weak solution for some hyperbolic conservation system
51 Matemáticas / Mathematics
Uniqueness
Suliciu relaxation system
Cauchy and Riemann problems
Global weak solutions
Delta shock solutions
Unicidad
Sistema de relajación de Suliciu
Problemas de Cauchy y Riemann
Soluciones débiles globales
Soluciones delta choques
title_short Uniqueness of global weak solution for some hyperbolic conservation system
title_full Uniqueness of global weak solution for some hyperbolic conservation system
title_fullStr Uniqueness of global weak solution for some hyperbolic conservation system
title_full_unstemmed Uniqueness of global weak solution for some hyperbolic conservation system
title_sort Uniqueness of global weak solution for some hyperbolic conservation system
dc.creator.fl_str_mv De la Cruz Guerrero, Richard Alexander
dc.contributor.author.spa.fl_str_mv De la Cruz Guerrero, Richard Alexander
dc.contributor.spa.fl_str_mv Rendón Arbeláez, Leonardo
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
Uniqueness
Suliciu relaxation system
Cauchy and Riemann problems
Global weak solutions
Delta shock solutions
Unicidad
Sistema de relajación de Suliciu
Problemas de Cauchy y Riemann
Soluciones débiles globales
Soluciones delta choques
dc.subject.proposal.spa.fl_str_mv Uniqueness
Suliciu relaxation system
Cauchy and Riemann problems
Global weak solutions
Delta shock solutions
Unicidad
Sistema de relajación de Suliciu
Problemas de Cauchy y Riemann
Soluciones débiles globales
Soluciones delta choques
description Abstract. In the present work, we study the uniqueness of entropy solutions for the Riemann and Cauchy problems associated to the Suliciu relaxation system where the initial data satisfies the conditions H1 and H2. Moreover, the solution is in L∞ space. Also, we show the explixit solutions for the Cauchy problem and generalized Riemann problem. When the condition H1 is not satisfied delta shock solutions are obtained for the Riemann problem associated to the Suliciu relaxation system. To guarantee uniqueness of delta shock solutions, we employ a generalization of the Rankine-Hugoniot condition together with a suitable entropy condition.
publishDate 2014
dc.date.issued.spa.fl_str_mv 2014
dc.date.accessioned.spa.fl_str_mv 2019-06-29T13:15:31Z
dc.date.available.spa.fl_str_mv 2019-06-29T13:15:31Z
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TD
format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/51990
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/46238/
url https://repositorio.unal.edu.co/handle/unal/51990
http://bdigital.unal.edu.co/46238/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Matemáticas
Departamento de Matemáticas
dc.relation.references.spa.fl_str_mv De la Cruz Guerrero, Richard Alexander (2014) Uniqueness of global weak solution for some hyperbolic conservation system. Doctorado thesis, Universidad Nacional de Colombia.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/51990/1/01830415.2014.pdf
https://repositorio.unal.edu.co/bitstream/unal/51990/2/01830415.2014.pdf.jpg
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
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