|本期目录/Table of Contents|

[1]冉丽霞,陈涌.耗散修正的CamassaHolm方程解的存在唯一性[J].浙江理工大学学报,2018,39-40(自科6):759-764.
 RAN Lixia,CHEN Yong.Existence and uniqueness of solution to the dissipation modified CamassaHolm equation[J].Journal of Zhejiang Sci-Tech University,2018,39-40(自科6):759-764.
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耗散修正的CamassaHolm方程解的存在唯一性()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第39-40卷
期数:
2018年自科6期
页码:
759-764
栏目:
出版日期:
2018-11-10

文章信息/Info

Title:
Existence and uniqueness of solution to the dissipation modified CamassaHolm equation
文章编号:
1673-3851 (2018) 11-0759-06
作者:
冉丽霞陈涌
浙江理工大学理学院,杭州 310018
Author(s):
RAN Lixia CHEN Yong
School of Sciences, Zhejiang Sci-Tech University,Hangzhou 310018, China
关键词:
修正的CamassaHolm方程存在性唯一性压缩映射
分类号:
O211.63
文献标志码:
A
摘要:
通过对修正的CamassaHolm方程添加耗散项ε 4xu,改进了其解的存在空间,证明了其在低正则性空间上解的存在唯一性。首先,通过Sobolev嵌入定理、Hlder不等式及傅里叶变换建立了非线性项的估计;其次,由压缩映射原理证明了解的局部存在唯一性;最后,由解的能量估计证明了整体解的存在性。结果表明:对于初值u0∈L2(R),耗散修正的CamassaHolm方程在空间C([0,T]:L2(R))∩L2((0,T):H2(R))存在唯一的局部解;进一步,对于初值u0∈H2(R),耗散修正的CamassaHolm方程在空间C([0,T]:L2(R))∩L2((0,T):H2(R))存在整体解。

参考文献/References:

[1] Constantin A, Kolev B. Geodesic flow on the diffeomorphism  group of the circle[J]. Commentarii Mathematici Helvetici,2003,78(4):787-804.
[2] Constantin A, Kolev B. Integrability of invariant metrics on  the diffeomorphism group of the circle[J]. Journal of Nonlinear Science,2006,16(2):109-122.
[3] Fokas A, Strauss W. Stability of peakons[J]. Communications  on Pure and Applied Mathematics,2000,53(5):603-610.
[4] Camassa R, Holm D. An integrable shallow water equations with peaked solutions[J]. Physical Review Letters,1993,71(11):1661-1664.
[5] Constantin A. On the Cauchy problem for the periodic CamassaHolm equation[J]. Journal of Differential  Equations,1997,141(2):218-235.
[6] Constantin A, Escher J. Global weak solutions for a shallow water equation[J]. Indiana University Mathematics Journal,1998,47(4):1527-1545.
[7] Misiolek G. Classical solutions of the periodic CamassaHolm equation[J]. Geometric and Functional Analysis Gafa,2002,12(5):1080-1104.
[8] Li Y, Olver P J. Wellposedness and blowup solutions for an integrable nonlinearly dispersive model wave equation[J]. Journal of Differential Equations,2000,162(1):27-63.
[9] Mclachlan R, Zhang X. Wellposedness of modified CamassaHolm equation[J]. Journal of Differential Equations,2009,246(8):3241-3259.
[10] Mu C L, Zhou S,Zeng R. Wellposedness and blowup phenomena for a higherorder shallow water equation[J]. Journal of Differential Equations,2011,251(12):3488-3499.

备注/Memo

备注/Memo:
收稿日期: 2018-05-24
网络出版日期: 2018-09-07
基金项目: 国家自然科学基金项目(11401532);浙江省自然科学基金项目(LY010027)
作者简介: 冉丽霞(1993-),女,甘肃陇南人,硕士研究生,主要从事随机偏微分方程方面的研究
通信作者: 陈涌,E-mail:youngchen329@126.com
更新日期/Last Update: 2018-11-14