Details
| Original language | English |
|---|---|
| Pages (from-to) | 479-508 |
| Number of pages | 30 |
| Journal | Journal of Functional Analysis |
| Volume | 256 |
| Issue number | 2 |
| Publication status | Published - 15 Jan 2009 |
Abstract
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.
Keywords
- Blow-up, Global existence, Initial boundary value problems, Local well-posedness, The Camassa-Holm equation and the rod equation, The Degasperis-Procesi equation and the b-equation
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Journal of Functional Analysis, Vol. 256, No. 2, 15.01.2009, p. 479-508.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Initial boundary value problems for nonlinear dispersive wave equations
AU - Escher, Joachim
AU - Yin, Zhaoyang
N1 - Funding information: The second author was partially supported by the Alexander von Humboldt Foundation, the NNSF of China (No. 10531040), the SRF for ROCS, SEM and the NSF of Guangdong Province. The authors thank the referee for valuable comments and suggestions.
PY - 2009/1/15
Y1 - 2009/1/15
N2 - 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.
AB - 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.
KW - Blow-up
KW - Global existence
KW - Initial boundary value problems
KW - Local well-posedness
KW - The Camassa-Holm equation and the rod equation
KW - The Degasperis-Procesi equation and the b-equation
UR - http://www.scopus.com/inward/record.url?scp=56549125309&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2008.07.010
DO - 10.1016/j.jfa.2008.07.010
M3 - Article
AN - SCOPUS:56549125309
VL - 256
SP - 479
EP - 508
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -