The study of global weak solutions for a generalized hyperelastic-rod wave equation
The global weak solution to the Cauchy problem for a generalized hyperelastic-rod wave equation (or the generalized Camassa–Holm equation) is investigated in the space C(|0, ∞) × R ∩ L∞ (|0, ∞); H1(R) under the assumption that the initial value u0(x) belongs to the space H1(R). The limit of the visc...
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| Format: | Journal Article |
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Elsevier
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/4790 |
| _version_ | 1848744615371341824 |
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| author | Lai, S. Wu, Yong Hong |
| author_facet | Lai, S. Wu, Yong Hong |
| author_sort | Lai, S. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The global weak solution to the Cauchy problem for a generalized hyperelastic-rod wave equation (or the generalized Camassa–Holm equation) is investigated in the space C(|0, ∞) × R ∩ L∞ (|0, ∞); H1(R) under the assumption that the initial value u0(x) belongs to the space H1(R). The limit of the viscous approximation for the equation is used to establish the existence of the global weak solution. The key elements in our analysis include 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. |
| first_indexed | 2025-11-14T06:04:17Z |
| format | Journal Article |
| id | curtin-20.500.11937-4790 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:04:17Z |
| publishDate | 2013 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-47902017-09-13T14:44:36Z The study of global weak solutions for a generalized hyperelastic-rod wave equation Lai, S. Wu, Yong Hong global weak solution generalized hyperelastic-rod wave equation existence The global weak solution to the Cauchy problem for a generalized hyperelastic-rod wave equation (or the generalized Camassa–Holm equation) is investigated in the space C(|0, ∞) × R ∩ L∞ (|0, ∞); H1(R) under the assumption that the initial value u0(x) belongs to the space H1(R). The limit of the viscous approximation for the equation is used to establish the existence of the global weak solution. The key elements in our analysis include 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. 2013 Journal Article http://hdl.handle.net/20.500.11937/4790 10.1016/j.na.2012.12.006 Elsevier restricted |
| spellingShingle | global weak solution generalized hyperelastic-rod wave equation existence Lai, S. Wu, Yong Hong The study of global weak solutions for a generalized hyperelastic-rod wave equation |
| title | The study of global weak solutions for a generalized hyperelastic-rod wave equation |
| title_full | The study of global weak solutions for a generalized hyperelastic-rod wave equation |
| title_fullStr | The study of global weak solutions for a generalized hyperelastic-rod wave equation |
| title_full_unstemmed | The study of global weak solutions for a generalized hyperelastic-rod wave equation |
| title_short | The study of global weak solutions for a generalized hyperelastic-rod wave equation |
| title_sort | study of global weak solutions for a generalized hyperelastic-rod wave equation |
| topic | global weak solution generalized hyperelastic-rod wave equation existence |
| url | http://hdl.handle.net/20.500.11937/4790 |