Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 256, Issue 2, Pages 479-508Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2008.07.010
Keywords
The Camassa-Holm equation and the rod equation; The Degasperis-Procesi equation and the b-equation; Initial boundary value problems; Local well-posedness; Blow-up; Global existence
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Funding
- Alexander von Humboldt Foundation
- NNSF of China [10531040]
- SRF for ROCS, SEM
- NSF of Guangdong Province
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In this paper we study initial Value boundary problems of two types of nonlinear dispersive wave equations on the half-line and on a finite interval subject to homogeneous Dirichlet boundary conditions. We first prove local well-posedness of the rod equation and of the b-equation for general initial data. Furthermore, we are able to specify conditions on the initial data which on the one hand guarantee global existence and on the other hand produce solutions with a finite life span. In the case of finite time singularities we are able to describe the precise blow-up scenario of breaking waves. Our approach is based on sharp extension results for functions on the half-line or on a finite interval and several symmetry preserving properties of the equations Under discussion. (C) 2008 Elsevier Inc. All rights reserved.
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