On the viscous Burgers equation in unbounded domain
In this paper we investigate the existence and uniqueness of global solutions, and a rate stability for the energy related with a Cauchy problem to the viscous Burgers equation in unbounded domain $\mathbb{R}\times(0,\infty)$. Some aspects associated with a Cauchy problem are presented in order to e...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2010-04-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=478 |
| _version_ | 1797830750129618944 |
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| author | Juan Limaco Haroldo Rodrigues Clark L. A. Medeiros |
| author_facet | Juan Limaco Haroldo Rodrigues Clark L. A. Medeiros |
| author_sort | Juan Limaco |
| collection | DOAJ |
| description | In this paper we investigate the existence and uniqueness of global solutions, and a rate stability for the energy related with a Cauchy problem to the viscous Burgers equation in unbounded domain $\mathbb{R}\times(0,\infty)$. Some aspects associated with a Cauchy problem are presented in order to employ the approximations of Faedo-Galerkin in whole real line $\mathbb{R}$. This becomes possible due to the introduction of weight Sobolev spaces which allow us to use arguments of compactness in the Sobolev spaces. |
| first_indexed | 2024-04-09T13:41:05Z |
| format | Article |
| id | doaj.art-f73f4775a2fc4ed291738a787e0647d3 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:05Z |
| publishDate | 2010-04-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-f73f4775a2fc4ed291738a787e0647d32023-05-09T07:53:00ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752010-04-0120101812310.14232/ejqtde.2010.1.18478On the viscous Burgers equation in unbounded domainJuan Limaco0Haroldo Rodrigues Clark1L. A. Medeiros2Universidade Federal Fluminense, Niteroi-RJ, BrazilUniversidade Federal Fluminense, Niteroi-RJ, BrazilUFRJ, Rio de Janeiro, BrasilIn this paper we investigate the existence and uniqueness of global solutions, and a rate stability for the energy related with a Cauchy problem to the viscous Burgers equation in unbounded domain $\mathbb{R}\times(0,\infty)$. Some aspects associated with a Cauchy problem are presented in order to employ the approximations of Faedo-Galerkin in whole real line $\mathbb{R}$. This becomes possible due to the introduction of weight Sobolev spaces which allow us to use arguments of compactness in the Sobolev spaces.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=478 |
| spellingShingle | Juan Limaco Haroldo Rodrigues Clark L. A. Medeiros On the viscous Burgers equation in unbounded domain Electronic Journal of Qualitative Theory of Differential Equations |
| title | On the viscous Burgers equation in unbounded domain |
| title_full | On the viscous Burgers equation in unbounded domain |
| title_fullStr | On the viscous Burgers equation in unbounded domain |
| title_full_unstemmed | On the viscous Burgers equation in unbounded domain |
| title_short | On the viscous Burgers equation in unbounded domain |
| title_sort | on the viscous burgers equation in unbounded domain |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=478 |
| work_keys_str_mv | AT juanlimaco ontheviscousburgersequationinunboundeddomain AT haroldorodriguesclark ontheviscousburgersequationinunboundeddomain AT lamedeiros ontheviscousburgersequationinunboundeddomain |