Global solutions and blow-up phenomena to a shallow water equation
A nonlinear shallow water equation, which includes the famous Camassa–Holm (CH) and Degasperis–Procesi (DP) equations as special cases, is investigated. The local well-posedness of solutions for the nonlinear equation in the Sobolev space Hs(R) with is developed. Provided that does not change sign...
| Main Authors: | , |
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| Format: | Journal Article |
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Elsevier BV
2010
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| Online Access: | http://hdl.handle.net/20.500.11937/37786 |
| _version_ | 1848755143552532480 |
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| author | Lai, S. Wu, Yonghong |
| author_facet | Lai, S. Wu, Yonghong |
| author_sort | Lai, S. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A nonlinear shallow water equation, which includes the famous Camassa–Holm (CH) and Degasperis–Procesi (DP) equations as special cases, is investigated. The local well-posedness of solutions for the nonlinear equation in the Sobolev space Hs(R) with is developed. Provided that does not change sign, u0∈Hs () and u0∈L1(R), the existence and uniqueness of the global solutions to the equation are shown to be true in u(t,x)∈C([0,∞);Hs(R))∩C1([0,∞);Hs−1(R)). Conditions that lead to the development of singularities in finite time for the solutions are also acquired. |
| first_indexed | 2025-11-14T08:51:37Z |
| format | Journal Article |
| id | curtin-20.500.11937-37786 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:51:37Z |
| publishDate | 2010 |
| publisher | Elsevier BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-377862017-09-13T15:57:54Z Global solutions and blow-up phenomena to a shallow water equation Lai, S. Wu, Yonghong Local well-posedness Global existence Shallow water model Blow-up A nonlinear shallow water equation, which includes the famous Camassa–Holm (CH) and Degasperis–Procesi (DP) equations as special cases, is investigated. The local well-posedness of solutions for the nonlinear equation in the Sobolev space Hs(R) with is developed. Provided that does not change sign, u0∈Hs () and u0∈L1(R), the existence and uniqueness of the global solutions to the equation are shown to be true in u(t,x)∈C([0,∞);Hs(R))∩C1([0,∞);Hs−1(R)). Conditions that lead to the development of singularities in finite time for the solutions are also acquired. 2010 Journal Article http://hdl.handle.net/20.500.11937/37786 10.1016/j.jde.2010.03.008 Elsevier BV unknown |
| spellingShingle | Local well-posedness Global existence Shallow water model Blow-up Lai, S. Wu, Yonghong Global solutions and blow-up phenomena to a shallow water equation |
| title | Global solutions and blow-up phenomena to a shallow water equation |
| title_full | Global solutions and blow-up phenomena to a shallow water equation |
| title_fullStr | Global solutions and blow-up phenomena to a shallow water equation |
| title_full_unstemmed | Global solutions and blow-up phenomena to a shallow water equation |
| title_short | Global solutions and blow-up phenomena to a shallow water equation |
| title_sort | global solutions and blow-up phenomena to a shallow water equation |
| topic | Local well-posedness Global existence Shallow water model Blow-up |
| url | http://hdl.handle.net/20.500.11937/37786 |