On the uniformly continuity of the solution map for two dimensional wave maps
The aim of this paper is to analyse the properties of the solution map to the Cauchy problem for the wave map equation with a source term, when the target is the hyperboloid ${\cal H}^2$ that is embedded in ${\cal R}^3$. The initial data are in ${\dot H}^1\times L^2$. We prove that the solution map...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2003-10-01
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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=166 |
| _version_ | 1797830754335457280 |
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| author | Svetlin Georgiev P. Georgieva |
| author_facet | Svetlin Georgiev P. Georgieva |
| author_sort | Svetlin Georgiev |
| collection | DOAJ |
| description | The aim of this paper is to analyse the properties of the solution map to the Cauchy problem for the wave map equation with a source term, when the target is the hyperboloid ${\cal H}^2$ that is embedded in ${\cal R}^3$. The initial data are in ${\dot H}^1\times L^2$. We prove that the solution map is not uniformly continuous. |
| first_indexed | 2024-04-09T13:41:10Z |
| format | Article |
| id | doaj.art-08bba0d221264bdb940dbdf2829f42b3 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:10Z |
| publishDate | 2003-10-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-08bba0d221264bdb940dbdf2829f42b32023-05-09T07:52:57ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752003-10-012003181710.14232/ejqtde.2003.1.18166On the uniformly continuity of the solution map for two dimensional wave mapsSvetlin Georgiev0P. Georgieva1University of Sofia, Sofia, BulgariaUniversity of Sofia, Sofia, BulgariaThe aim of this paper is to analyse the properties of the solution map to the Cauchy problem for the wave map equation with a source term, when the target is the hyperboloid ${\cal H}^2$ that is embedded in ${\cal R}^3$. The initial data are in ${\dot H}^1\times L^2$. We prove that the solution map is not uniformly continuous.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=166 |
| spellingShingle | Svetlin Georgiev P. Georgieva On the uniformly continuity of the solution map for two dimensional wave maps Electronic Journal of Qualitative Theory of Differential Equations |
| title | On the uniformly continuity of the solution map for two dimensional wave maps |
| title_full | On the uniformly continuity of the solution map for two dimensional wave maps |
| title_fullStr | On the uniformly continuity of the solution map for two dimensional wave maps |
| title_full_unstemmed | On the uniformly continuity of the solution map for two dimensional wave maps |
| title_short | On the uniformly continuity of the solution map for two dimensional wave maps |
| title_sort | on the uniformly continuity of the solution map for two dimensional wave maps |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=166 |
| work_keys_str_mv | AT svetlingeorgiev ontheuniformlycontinuityofthesolutionmapfortwodimensionalwavemaps AT pgeorgieva ontheuniformlycontinuityofthesolutionmapfortwodimensionalwavemaps |