Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 87-117 |
| Seitenumfang | 31 |
| Fachzeitschrift | Indiana University Mathematics Journal |
| Jahrgang | 56 |
| Ausgabenummer | 1 |
| Publikationsstatus | Veröffentlicht - 2007 |
Abstract
In this paper we mainly study the problem of the development of singularities for solutions to the periodic Degasperis-Procesi equation. Firstly, we show that the first blow-up of strong solution to the equation must occur only in the form of wave breaking and shock waves possibly appear afterwards. Secondly, we established two new blow-up results. Thirdly, we investigate the blow-up rate for all non-global strong solutions and determine the blow-up set of blowing-up strong solutions to the equation for a large class of initial data. We finally give an explicit example of weak solutions to the equation, which may be considered as periodic shock waves.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Indiana University Mathematics Journal, Jahrgang 56, Nr. 1, 2007, S. 87-117.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation
AU - Escher, Joachim
AU - Liu, Yue
AU - Yin, Zhaoyang
PY - 2007
Y1 - 2007
N2 - In this paper we mainly study the problem of the development of singularities for solutions to the periodic Degasperis-Procesi equation. Firstly, we show that the first blow-up of strong solution to the equation must occur only in the form of wave breaking and shock waves possibly appear afterwards. Secondly, we established two new blow-up results. Thirdly, we investigate the blow-up rate for all non-global strong solutions and determine the blow-up set of blowing-up strong solutions to the equation for a large class of initial data. We finally give an explicit example of weak solutions to the equation, which may be considered as periodic shock waves.
AB - In this paper we mainly study the problem of the development of singularities for solutions to the periodic Degasperis-Procesi equation. Firstly, we show that the first blow-up of strong solution to the equation must occur only in the form of wave breaking and shock waves possibly appear afterwards. Secondly, we established two new blow-up results. Thirdly, we investigate the blow-up rate for all non-global strong solutions and determine the blow-up set of blowing-up strong solutions to the equation for a large class of initial data. We finally give an explicit example of weak solutions to the equation, which may be considered as periodic shock waves.
KW - Blow-up rate
KW - Blow-up set
KW - Periodic Degasperis-Procesi equation
KW - Periodic peakons
KW - Periodic shock waves
UR - http://www.scopus.com/inward/record.url?scp=34247509833&partnerID=8YFLogxK
U2 - 10.1512/iumj.2007.56.3040
DO - 10.1512/iumj.2007.56.3040
M3 - Article
AN - SCOPUS:34247509833
VL - 56
SP - 87
EP - 117
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
SN - 0022-2518
IS - 1
ER -