The H1(R) Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation
The existence of global weak solutions to the Cauchy problem for a generalized Camassa-Holm equation with a dissipative term is investigated in the space C([0,∞) × R)∩L∞([0,∞); H1(R)) provided that its initial value u0(x) belongs to the space H1(R). A one-sided super bound estimate and a space-time...
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| Main Authors: | , , , |
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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/10.1155/2012/693010 |
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| _version_ | 1850176725115207680 |
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| author | Zhaowei Sheng Shaoyong Lai Yuan Ma Xuanjun Luo |
| author_facet | Zhaowei Sheng Shaoyong Lai Yuan Ma Xuanjun Luo |
| author_sort | Zhaowei Sheng |
| collection | DOAJ |
| description | The existence of global weak solutions to the Cauchy problem for a generalized Camassa-Holm equation with a dissipative term is investigated in the space C([0,∞) × R)∩L∞([0,∞); H1(R)) provided that its initial value u0(x) belongs to the space H1(R). A one-sided super bound estimate and a space-time higher-norm estimate on the first-order derivatives of the solution with respect to the space variable are derived. |
| format | Article |
| id | doaj-art-bddaf30dbb0f422dbd28c443edc6bc15 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bddaf30dbb0f422dbd28c443edc6bc152025-08-20T02:19:12ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/693010693010The H1(R) Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm EquationZhaowei Sheng0Shaoyong Lai1Yuan Ma2Xuanjun Luo3Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaDepartment of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaDepartment of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaDepartment of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaThe existence of global weak solutions to the Cauchy problem for a generalized Camassa-Holm equation with a dissipative term is investigated in the space C([0,∞) × R)∩L∞([0,∞); H1(R)) provided that its initial value u0(x) belongs to the space H1(R). A one-sided super bound estimate and a space-time higher-norm estimate on the first-order derivatives of the solution with respect to the space variable are derived.http://dx.doi.org/10.1155/2012/693010 |
| spellingShingle | Zhaowei Sheng Shaoyong Lai Yuan Ma Xuanjun Luo The H1(R) Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation Abstract and Applied Analysis |
| title | The H1(R) Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation |
| title_full | The H1(R) Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation |
| title_fullStr | The H1(R) Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation |
| title_full_unstemmed | The H1(R) Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation |
| title_short | The H1(R) Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation |
| title_sort | h1 r space global weak solutions to the weakly dissipative camassa holm equation |
| url | http://dx.doi.org/10.1155/2012/693010 |
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