On the uniqueness and large time behavior of the weak solutions to a shallow water equation

doi:10.1081/pde-120016129

CSpace

	On the uniqueness and large time behavior of the weak solutions to a shallow water equation
	Xin, ZP ; Zhang, P
	2002
发表期刊	COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0360-5302
卷号	27 期号:9-10 页码:1815-1844
摘要	We obtain a "weak = strong" theorem for the admissible weak solutions, constructed by the authors in (Zhouping Xin; Ping Zhang. On the Weak Solutions to Shallow Water. Equations. Comm. Pure Appl. Math. 2000, 53, 1411-1433.) to a shallow water equation. In particular, this result implies the uniqueness of weak solution to this equation when u(0) is an element of H-1 and m(0) = u(0) - partial derivative(xx)u(0) is a positive Radon measure. Moreover, with additional assumption on the solutions, we prove that the admissible weak solutions constructed in, (Zhouping Xin; Ping Zhang. On the Weak Solutions to Shallow Water Equations Comm. Pure Appl. Math. 2000, 53, 1411-1433.) tend to 0 pointwisely as t --> infinity.
关键词	shallow water equation weak solutions uniqueness
DOI	10.1081/pde-120016129
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000179798400004
出版者	MARCEL DEKKER INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17742
专题	中国科学院数学与系统科学研究院
通讯作者	Xin, ZP
作者单位	1.Chinese Univ Hong Kong, Inst Math Sci, Hong Kong, Hong Kong, Peoples R China 2.NYU, Courant Inst, New York, NY USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Xin, ZP,Zhang, P. On the uniqueness and large time behavior of the weak solutions to a shallow water equation[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,2002,27(9-10):1815-1844.
APA	Xin, ZP,&Zhang, P.(2002).On the uniqueness and large time behavior of the weak solutions to a shallow water equation.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,27(9-10),1815-1844.
MLA	Xin, ZP,et al."On the uniqueness and large time behavior of the weak solutions to a shallow water equation".COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 27.9-10(2002):1815-1844.