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1.Blow up of Solutions and Traveling Waves to the Two-Component mu-Camassa-Holm System
×÷Õß: Zhang, Y (Zhang, Ying)[ 1 ] ; Liu, Y (Liu, Yue)[ 2,3 ] ; Qu, CZ (Qu, Changzheng)[ 3 ]
À´Ô´³ö°æÎï: INTERNATIONAL MATHEMATICS RESEARCH NOTICES ÆÚ: 15 Ò³: 3386-3419 DOI: 10.1093/imrn/rns150 ³ö°æÄê: 2013
±»ÒýƵ´Î: 0 (À´×Ô Web of Science)
ÒýÓõIJο¼ÎÄÏ×: 54 [ ²é¿´ Related Records ] ÒýÖ¤¹ØÏµÍ¼
ÕªÒª: The integrable two-component mu-Camassa-Holm system is a mid-way system between the two-component Camassa-Holm and the two-component Hunter-Saxton systems. The initial-value problem and traveling-wave solutions to the two-component mu-Camassa-Holm system in the periodic setting are investigated in this paper. Blow-up scenarios for strong solutions are established. Several blow-up data and blow-up rate for strong solutions are provided. Finally, the existence of smooth periodic traveling-wave solutions is determined.
Èë²ØºÅ: WOS:000322344100002
ÎÄÏ×ÀàÐÍ: Article
ÓïÖÖ: English
KeyWords Plus: SHALLOW-WATER EQUATION; HUNTER-SAXTON EQUATION; HYPERBOLIC VARIATIONAL EQUATION; DEGASPERIS-PROCESI EQUATIONS; GLOBAL EXISTENCE; GEODESIC-FLOW; WELL-POSEDNESS; WEAK SOLUTIONS; BREAKING; SOLITONS
ͨѶ×÷ÕßµØÖ·: Liu, Y (ͨѶ×÷Õß)
Univ Texas Arlington, Dept Math, Arlington, TX 76019 USA.
µØÖ·:
[ 1 ] NW Univ Xian, Dept Math, Xian 710069, Peoples R China
[ 2 ] Univ Texas Arlington, Dept Math, Arlington, TX 76019 USA
[ 3 ] Ningbo Univ, Dept Math, Ningbo 315211, Zhejiang, Peoples R China
µç×ÓÓʼþµØÖ·: yliu@uta.edu
»ù½ð×ÊÖúÖÂл:
»ù½ð×ÊÖú»ú¹¹ ÊÚȨºÅ
NSF
DMS-0906099
NSF-China for Distinguished Young Scholars
003599-0001-2009
10925104
[ÏÔʾ»ù½ð×ÊÖúÐÅÏ¢]
³ö°æÉÌ: OXFORD UNIV PRESS, GREAT CLARENDON ST, OXFORD OX2 6DP, ENGLAND
Web of Science Àà±ð: Mathematics
Ñо¿·½Ïò: Mathematics
IDS ºÅ: 190ML
ISSN: 1073-7928
2.Global weak solutions for a periodic two-component -Camassa-Holm system
×÷Õß: Zhang, Y (Zhang, Ying)[ 1,2 ]
À´Ô´³ö°æÎï: MATHEMATICAL METHODS IN THE APPLIED SCIENCES ¾í: 36 ÆÚ: 13 Ò³: 1734-1745 DOI: 10.1002/mma.2719 ³ö°æÄê: SEP 15 2013
±»ÒýƵ´Î: 0 (À´×Ô Web of Science)
ÒýÓõIJο¼ÎÄÏ×: 29 [ ²é¿´ Related Records ] ÒýÖ¤¹ØÏµÍ¼
ÕªÒª: In this paper, we consider the global existence of weak solutions for a two-component -Camassa-Holm system in the periodic setting. Global existence for strong solutions to the system with smooth approximate initial value is derived. -Camassa-Holm system. Copyright (c) 2013 John Wiley & Sons, Ltd.
Èë²ØºÅ: WOS:000322221700007
ÎÄÏ×ÀàÐÍ: Article
ÓïÖÖ: English
×÷Õ߹ؼü´Ê: generalized Camassa-Holm system; weak solutions; approximate solutions; global existence
KeyWords Plus: SHALLOW-WATER EQUATION; BLOW-UP; SOLITONS
ͨѶ×÷ÕßµØÖ·: Zhang, Y (ͨѶ×÷Õß)
NW Univ Xian, Dept Math, Xian 710069, Peoples R China.
µØÖ·:
[ 1 ] NW Univ Xian, Dept Math, Xian 710069, Peoples R China
[ 2 ] Tianshui Normal Univ, Sch Math & Stat, Tianshui 741001, Peoples R China
µç×ÓÓʼþµØÖ·: zwbandzy@163.com
»ù½ð×ÊÖúÖÂл:
»ù½ð×ÊÖú»ú¹¹ ÊÚȨºÅ
NSF of China
11101332
Program of Shaanxi Provincial Department of Education
11JK0482
[ÏÔʾ»ù½ð×ÊÖúÐÅÏ¢]
³ö°æÉÌ: WILEY-BLACKWELL, 111 RIVER ST, HOBOKEN 07030-5774, NJ USA
Web of Science Àà±ð: Mathematics, Applied
Ñо¿·½Ïò: Mathematics
IDS ºÅ: 188UX
ISSN: 0170-4214 |
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