Global solutions and blow-up phenomena to a shallow water equation
| dc.contributor.author | Lai, S. | |
| dc.contributor.author | Wu, Yonghong | |
| dc.date.accessioned | 2017-01-30T14:07:52Z | |
| dc.date.available | 2017-01-30T14:07:52Z | |
| dc.date.created | 2011-03-24T20:01:33Z | |
| dc.date.issued | 2010 | |
| dc.identifier.citation | Lai, Shaoyong and Wu, Yonghong. 2010. Global solutions and blow-up phenomena to a shallow water equation. Journal of Differential Equations. 249 (3): pp. 693-706. | |
| dc.identifier.uri | http://hdl.handle.net/20.500.11937/37786 | |
| dc.identifier.doi | 10.1016/j.jde.2010.03.008 | |
| dc.description.abstract |
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. | |
| dc.publisher | Elsevier BV | |
| dc.subject | Local well-posedness | |
| dc.subject | Global existence | |
| dc.subject | Shallow water model | |
| dc.subject | Blow-up | |
| dc.title | Global solutions and blow-up phenomena to a shallow water equation | |
| dc.type | Journal Article | |
| dcterms.source.volume | 249 | |
| dcterms.source.startPage | 693 | |
| dcterms.source.endPage | 706 | |
| dcterms.source.issn | 00220396 | |
| dcterms.source.title | Journal of Differential Equations | |
| curtin.department | Department of Mathematics and Statistics | |
| curtin.accessStatus | Open access via publisher |