Details
| Original language | English |
|---|---|
| Pages (from-to) | 457-485 |
| Number of pages | 29 |
| Journal | Journal of Functional Analysis |
| Volume | 241 |
| Issue number | 2 |
| Publication status | Published - 15 Dec 2006 |
Abstract
In this paper we study several qualitative properties of the Degasperis-Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions.
Keywords
- Blow-up rate, Blow-up set, Degasperis-Procesi equation, Global weak solutions
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Journal of Functional Analysis, Vol. 241, No. 2, 15.12.2006, p. 457-485.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Global weak solutions and blow-up structure for the Degasperis-Procesi equation
AU - Escher, Joachim
AU - Liu, Yue
AU - Yin, Zhaoyang
N1 - Funding information: The authors gratefully acknowledge the hospitality and support of the Mittag-Leffler Institute during the program on Wave Motion in the Fall of 2005. Liu is grateful to the DFG for financial support through respectively the Graduiertenkolleg 615 “Interaction of Modeling, Computation Methods and Software Concepts for Scientific-Technological Problem”. Yin was partially supported by the Alexander von Humboldt Foundation, the NNSF of China (No. 10531040), the NSF of Guangdong Province, and the Foundation of Zhongshan University Advanced Research Center. The authors also thank the anonymous referee for valuable comments and suggestions.
PY - 2006/12/15
Y1 - 2006/12/15
N2 - In this paper we study several qualitative properties of the Degasperis-Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions.
AB - In this paper we study several qualitative properties of the Degasperis-Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions.
KW - Blow-up rate
KW - Blow-up set
KW - Degasperis-Procesi equation
KW - Global weak solutions
UR - http://www.scopus.com/inward/record.url?scp=33750014750&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2006.03.022
DO - 10.1016/j.jfa.2006.03.022
M3 - Article
AN - SCOPUS:33750014750
VL - 241
SP - 457
EP - 485
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -