A model containing both the Camassa–Holm and Degasperis–Procesi equations
A nonlinear dispersive partial differential equation, which includes the famous Camassa–Holm and Degasperis–Procesi equations as special cases, is investigated. Although the H1-norm of the solutions to the nonlinear model does not remain constants, the existence of its weak solutions in lower order...
| Main Authors: | , |
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| Format: | Journal Article |
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Academic Press
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/7358 |
| _version_ | 1848745346257125376 |
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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 | A nonlinear dispersive partial differential equation, which includes the famous Camassa–Holm and Degasperis–Procesi equations as special cases, is investigated. Although the H1-norm of the solutions to the nonlinear model does not remain constants, the existence of its weak solutions in lower order Sobolev space Hs with 1 < s <= 3/2 is established under the assumptions u0 ε Hs and t norm of ||u0x||L∞ < ∞. The local well-posedness of solutions for the equation in the Sobolev space Hs(R) with s > 3/2 is also developed. |
| first_indexed | 2025-11-14T06:15:54Z |
| format | Journal Article |
| id | curtin-20.500.11937-7358 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:15:54Z |
| publishDate | 2011 |
| publisher | Academic Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-73582017-09-13T16:09:21Z A model containing both the Camassa–Holm and Degasperis–Procesi equations Lai, S. Wu, Yong Hong Local well-posedness Camassa–Holm equation Weak solution Degasperis–Procesi A nonlinear dispersive partial differential equation, which includes the famous Camassa–Holm and Degasperis–Procesi equations as special cases, is investigated. Although the H1-norm of the solutions to the nonlinear model does not remain constants, the existence of its weak solutions in lower order Sobolev space Hs with 1 < s <= 3/2 is established under the assumptions u0 ε Hs and t norm of ||u0x||L∞ < ∞. The local well-posedness of solutions for the equation in the Sobolev space Hs(R) with s > 3/2 is also developed. 2011 Journal Article http://hdl.handle.net/20.500.11937/7358 10.1016/j.jmaa.2010.09.012 Academic Press unknown |
| spellingShingle | Local well-posedness Camassa–Holm equation Weak solution Degasperis–Procesi Lai, S. Wu, Yong Hong A model containing both the Camassa–Holm and Degasperis–Procesi equations |
| title | A model containing both the Camassa–Holm and Degasperis–Procesi equations |
| title_full | A model containing both the Camassa–Holm and Degasperis–Procesi equations |
| title_fullStr | A model containing both the Camassa–Holm and Degasperis–Procesi equations |
| title_full_unstemmed | A model containing both the Camassa–Holm and Degasperis–Procesi equations |
| title_short | A model containing both the Camassa–Holm and Degasperis–Procesi equations |
| title_sort | model containing both the camassa–holm and degasperis–procesi equations |
| topic | Local well-posedness Camassa–Holm equation Weak solution Degasperis–Procesi |
| url | http://hdl.handle.net/20.500.11937/7358 |