Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗
We consider the generalized Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the scalar conservation law. The proof relies on deriving...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2016-03-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/808 |
| _version_ | 1818387709893279744 |
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| author | Giuseppe Maria Coclite Lorenzo di Ruvo |
| author_facet | Giuseppe Maria Coclite Lorenzo di Ruvo |
| author_sort | Giuseppe Maria Coclite |
| collection | DOAJ |
| description | We consider the generalized Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting. |
| first_indexed | 2024-12-14T04:14:16Z |
| format | Article |
| id | doaj.art-5017468a15454e52b9faacb8beaab939 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-14T04:14:16Z |
| publishDate | 2016-03-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-5017468a15454e52b9faacb8beaab9392022-12-21T23:17:35ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102016-03-0121210.3846/13926292.2016.1150358Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗Giuseppe Maria Coclite0Lorenzo di Ruvo1Department of Mathematics, University of Bari via E. Orabona 4, 70125 Bari, ItalyDepartment of Science and Methods for Engineering, University of Modena and Reggio Emilia via G. Amendola 2, 42122 Reggio Emilia, ItalyWe consider the generalized Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting.https://journals.vgtu.lt/index.php/MMA/article/view/808singular limitcompensated compactnessconnected compactnessKorteweg-de Vries equation |
| spellingShingle | Giuseppe Maria Coclite Lorenzo di Ruvo Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗ Mathematical Modelling and Analysis singular limit compensated compactness connected compactness Korteweg-de Vries equation |
| title | Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗ |
| title_full | Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗ |
| title_fullStr | Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗ |
| title_full_unstemmed | Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗ |
| title_short | Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗ |
| title_sort | convergence of the solutions on the generalized korteweg de vries equation∗ |
| topic | singular limit compensated compactness connected compactness Korteweg-de Vries equation |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/808 |
| work_keys_str_mv | AT giuseppemariacoclite convergenceofthesolutionsonthegeneralizedkortewegdevriesequation AT lorenzodiruvo convergenceofthesolutionsonthegeneralizedkortewegdevriesequation |