Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System
The global solutions of the perturbed Riemann problem for the Leroux system are constructed explicitly under the suitable assumptions when the initial data are taken to be three piecewise constant states. The wave interaction problems are widely investigated during the process of constructing global...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/4808610 |
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| _version_ | 1832547011040116736 |
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| author | Pengpeng Ji Chun Shen |
| author_facet | Pengpeng Ji Chun Shen |
| author_sort | Pengpeng Ji |
| collection | DOAJ |
| description | The global solutions of the perturbed Riemann problem for the Leroux system are constructed explicitly under the suitable assumptions when the initial data are taken to be three piecewise constant states. The wave interaction problems are widely investigated during the process of constructing global solutions with the help of the geometrical structures of the shock and rarefaction curves in the phase plane. In addition, it is shown that the Riemann solutions are stable with respect to the specific small perturbations of the Riemann initial data. |
| format | Article |
| id | doaj-art-624f8a51448640e598807bd90e5c36be |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-624f8a51448640e598807bd90e5c36be2025-02-03T06:46:17ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/48086104808610Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux SystemPengpeng Ji0Chun Shen1School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, ChinaSchool of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, ChinaThe global solutions of the perturbed Riemann problem for the Leroux system are constructed explicitly under the suitable assumptions when the initial data are taken to be three piecewise constant states. The wave interaction problems are widely investigated during the process of constructing global solutions with the help of the geometrical structures of the shock and rarefaction curves in the phase plane. In addition, it is shown that the Riemann solutions are stable with respect to the specific small perturbations of the Riemann initial data.http://dx.doi.org/10.1155/2016/4808610 |
| spellingShingle | Pengpeng Ji Chun Shen Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System Advances in Mathematical Physics |
| title | Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System |
| title_full | Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System |
| title_fullStr | Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System |
| title_full_unstemmed | Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System |
| title_short | Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System |
| title_sort | construction of the global solutions to the perturbed riemann problem for the leroux system |
| url | http://dx.doi.org/10.1155/2016/4808610 |
| work_keys_str_mv | AT pengpengji constructionoftheglobalsolutionstotheperturbedriemannproblemforthelerouxsystem AT chunshen constructionoftheglobalsolutionstotheperturbedriemannproblemforthelerouxsystem |