Existence of traveling waves for diffusive-dispersive conservation laws
In this work we show the existence existence and uniqueness of traveling waves for diffusive-dispersive conservation laws with flux function in $C^{1}(mathbb{R})$, by using phase plane analysis. Also we estimate the domain of attraction of the equilibrium point attractor corresponding to the rig...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2013-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/39/abstr.html |
| _version_ | 1831679984284991488 |
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| author | Cezar I. Kondo Alex F. Rossini |
| author_facet | Cezar I. Kondo Alex F. Rossini |
| author_sort | Cezar I. Kondo |
| collection | DOAJ |
| description | In this work we show the existence existence and uniqueness of traveling waves for diffusive-dispersive conservation laws with flux function in $C^{1}(mathbb{R})$, by using phase plane analysis. Also we estimate the domain of attraction of the equilibrium point attractor corresponding to the right-hand state. The equilibrium point corresponding to the left-hand state is a saddle point. According to the phase portrait close to the saddle point, there are exactly two semi-orbits of the system. We establish that only one semi-orbit come in the domain of attraction and converges to $(u_{-},0)$ as $yo -infty$. This provides the desired saddle-attractor connection. |
| first_indexed | 2024-12-20T05:29:25Z |
| format | Article |
| id | doaj.art-3385750b40284452bbe89ac7a2f71b6b |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T05:29:25Z |
| publishDate | 2013-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3385750b40284452bbe89ac7a2f71b6b2022-12-21T19:51:47ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-02-01201339,114Existence of traveling waves for diffusive-dispersive conservation lawsCezar I. KondoAlex F. RossiniIn this work we show the existence existence and uniqueness of traveling waves for diffusive-dispersive conservation laws with flux function in $C^{1}(mathbb{R})$, by using phase plane analysis. Also we estimate the domain of attraction of the equilibrium point attractor corresponding to the right-hand state. The equilibrium point corresponding to the left-hand state is a saddle point. According to the phase portrait close to the saddle point, there are exactly two semi-orbits of the system. We establish that only one semi-orbit come in the domain of attraction and converges to $(u_{-},0)$ as $yo -infty$. This provides the desired saddle-attractor connection.http://ejde.math.txstate.edu/Volumes/2013/39/abstr.htmlScalar conservation lawdiffusive-dispersiveweak solutiontraveling wavephase portrait |
| spellingShingle | Cezar I. Kondo Alex F. Rossini Existence of traveling waves for diffusive-dispersive conservation laws Electronic Journal of Differential Equations Scalar conservation law diffusive-dispersive weak solution traveling wave phase portrait |
| title | Existence of traveling waves for diffusive-dispersive conservation laws |
| title_full | Existence of traveling waves for diffusive-dispersive conservation laws |
| title_fullStr | Existence of traveling waves for diffusive-dispersive conservation laws |
| title_full_unstemmed | Existence of traveling waves for diffusive-dispersive conservation laws |
| title_short | Existence of traveling waves for diffusive-dispersive conservation laws |
| title_sort | existence of traveling waves for diffusive dispersive conservation laws |
| topic | Scalar conservation law diffusive-dispersive weak solution traveling wave phase portrait |
| url | http://ejde.math.txstate.edu/Volumes/2013/39/abstr.html |
| work_keys_str_mv | AT cezarikondo existenceoftravelingwavesfordiffusivedispersiveconservationlaws AT alexfrossini existenceoftravelingwavesfordiffusivedispersiveconservationlaws |