The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term
A shallow water wave equation with a weakly dissipative term, which includes the weakly dissipative Camassa-Holm and the weakly dissipative Degasperis-Procesi equations as special cases, is investigated. The sufficient conditions about the existence of the global strong solution are given. Provided...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/840919 |
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| _version_ | 1832556712407597056 |
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| author | Ying Wang YunXi Guo |
| author_facet | Ying Wang YunXi Guo |
| author_sort | Ying Wang |
| collection | DOAJ |
| description | A shallow water wave equation with a weakly dissipative term, which includes the weakly dissipative Camassa-Holm and the weakly dissipative Degasperis-Procesi equations as special cases, is investigated. The sufficient conditions about the existence of the global strong solution are given. Provided that (1-∂x2)u0∈M+(R), u0∈H1(R), and u0∈L1(R), the existence and uniqueness of the global weak solution to the equation are shown to be true. |
| format | Article |
| id | doaj-art-e2d4dd8d590b4c419a17f38cb5dc1ee5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e2d4dd8d590b4c419a17f38cb5dc1ee52025-02-03T05:44:39ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/840919840919The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative TermYing Wang0YunXi Guo1College of Science, Sichuan University of Science and Engineering, Zigong 643000, ChinaCollege of Science, Sichuan University of Science and Engineering, Zigong 643000, ChinaA shallow water wave equation with a weakly dissipative term, which includes the weakly dissipative Camassa-Holm and the weakly dissipative Degasperis-Procesi equations as special cases, is investigated. The sufficient conditions about the existence of the global strong solution are given. Provided that (1-∂x2)u0∈M+(R), u0∈H1(R), and u0∈L1(R), the existence and uniqueness of the global weak solution to the equation are shown to be true.http://dx.doi.org/10.1155/2012/840919 |
| spellingShingle | Ying Wang YunXi Guo The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term Abstract and Applied Analysis |
| title | The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term |
| title_full | The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term |
| title_fullStr | The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term |
| title_full_unstemmed | The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term |
| title_short | The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term |
| title_sort | cauchy problem to a shallow water wave equation with a weakly dissipative term |
| url | http://dx.doi.org/10.1155/2012/840919 |
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