Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval
We study the initial boundary value problem of the general three-component Camassa-Holm shallow water system on an interval subject to inhomogeneous boundary conditions. First we prove a local in time existence theorem and present a weak-strong uniqueness result. Then, we establish a asymptotic stab...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/691731 |
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| _version_ | 1832564417617723392 |
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| author | Lixin Tian Qingwen Yuan Lizhen Wang |
| author_facet | Lixin Tian Qingwen Yuan Lizhen Wang |
| author_sort | Lixin Tian |
| collection | DOAJ |
| description | We study the initial boundary value problem of the general three-component
Camassa-Holm shallow water system on an interval subject to inhomogeneous
boundary conditions. First we prove a local in time existence theorem and
present a weak-strong uniqueness result. Then, we establish a asymptotic stabilization
of this system by a boundary feedback. Finally, we obtain a result of blow-up
solution with certain initial data and boundary profiles. |
| format | Article |
| id | doaj-art-96efd6faa3954ae3ad65a22f0635cde1 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-96efd6faa3954ae3ad65a22f0635cde12025-02-03T01:11:09ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/691731691731Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an IntervalLixin Tian0Qingwen Yuan1Lizhen Wang2Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaNonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaNonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaWe study the initial boundary value problem of the general three-component Camassa-Holm shallow water system on an interval subject to inhomogeneous boundary conditions. First we prove a local in time existence theorem and present a weak-strong uniqueness result. Then, we establish a asymptotic stabilization of this system by a boundary feedback. Finally, we obtain a result of blow-up solution with certain initial data and boundary profiles.http://dx.doi.org/10.1155/2013/691731 |
| spellingShingle | Lixin Tian Qingwen Yuan Lizhen Wang Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval Journal of Function Spaces and Applications |
| title | Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval |
| title_full | Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval |
| title_fullStr | Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval |
| title_full_unstemmed | Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval |
| title_short | Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval |
| title_sort | initial boundary value problem of the general three component camassa holm shallow water system on an interval |
| url | http://dx.doi.org/10.1155/2013/691731 |
| work_keys_str_mv | AT lixintian initialboundaryvalueproblemofthegeneralthreecomponentcamassaholmshallowwatersystemonaninterval AT qingwenyuan initialboundaryvalueproblemofthegeneralthreecomponentcamassaholmshallowwatersystemonaninterval AT lizhenwang initialboundaryvalueproblemofthegeneralthreecomponentcamassaholmshallowwatersystemonaninterval |