Colombeau's theory and shock wave solutions for systems of PDEs
Autor(a) principal: | |
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Data de Publicação: | 2000 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | https://eudml.org/doc/121151 http://hdl.handle.net/11449/10505 |
Resumo: | In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association. |
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Repositório Institucional da UNESP |
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2946 |
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Colombeau's theory and shock wave solutions for systems of PDEsShock wave solutionGeneralized functionDistributionIn this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.UNESP, FEIS, Dept Matemat, BR-15385000 Ilha Solteira, SP, BrazilUNESP, FEIS, Dept Matemat, BR-15385000 Ilha Solteira, SP, BrazilTexas State UnivUniversidade Estadual Paulista (Unesp)Villarreal, F.2014-05-20T13:30:52Z2014-05-20T13:30:52Z2000-03-12info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article17https://eudml.org/doc/121151Electronic Journal of Differential Equations. San Marcos: Texas State Univ, 17 p., 2000.1072-6691http://hdl.handle.net/11449/10505WOS:000208498700002Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengElectronic Journal of Differential Equations0.9440,538info:eu-repo/semantics/openAccess2024-07-10T15:41:53Zoai:repositorio.unesp.br:11449/10505Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:04:13.174794Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Colombeau's theory and shock wave solutions for systems of PDEs |
title |
Colombeau's theory and shock wave solutions for systems of PDEs |
spellingShingle |
Colombeau's theory and shock wave solutions for systems of PDEs Villarreal, F. Shock wave solution Generalized function Distribution |
title_short |
Colombeau's theory and shock wave solutions for systems of PDEs |
title_full |
Colombeau's theory and shock wave solutions for systems of PDEs |
title_fullStr |
Colombeau's theory and shock wave solutions for systems of PDEs |
title_full_unstemmed |
Colombeau's theory and shock wave solutions for systems of PDEs |
title_sort |
Colombeau's theory and shock wave solutions for systems of PDEs |
author |
Villarreal, F. |
author_facet |
Villarreal, F. |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Villarreal, F. |
dc.subject.por.fl_str_mv |
Shock wave solution Generalized function Distribution |
topic |
Shock wave solution Generalized function Distribution |
description |
In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association. |
publishDate |
2000 |
dc.date.none.fl_str_mv |
2000-03-12 2014-05-20T13:30:52Z 2014-05-20T13:30:52Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://eudml.org/doc/121151 Electronic Journal of Differential Equations. San Marcos: Texas State Univ, 17 p., 2000. 1072-6691 http://hdl.handle.net/11449/10505 WOS:000208498700002 |
url |
https://eudml.org/doc/121151 http://hdl.handle.net/11449/10505 |
identifier_str_mv |
Electronic Journal of Differential Equations. San Marcos: Texas State Univ, 17 p., 2000. 1072-6691 WOS:000208498700002 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Electronic Journal of Differential Equations 0.944 0,538 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
17 |
dc.publisher.none.fl_str_mv |
Texas State Univ |
publisher.none.fl_str_mv |
Texas State Univ |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129487316975616 |