On oscillations of an asymptotic equation of a nonlinear variational wave equation

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	On oscillations of an asymptotic equation of a nonlinear variational wave equation
	Zhang, P ; Zheng, YX
	1998-12-01
发表期刊	ASYMPTOTIC ANALYSIS
ISSN	0921-7134
卷号	18 期号:3-4 页码:307-327
摘要	The wave equation partial derivative(t)(2)u - c partial derivative(x)(c partial derivative(x)u) = 0, where c = c(u) is a given function, arises in a number of different physical contexts and is the simplest example of an interesting class of nonlinear hyperbolic partial differential equations. For unidirectional weakly nonlinear waves, an asymptotic equation partial derivative(x)(partial derivative(t)u + u partial derivative(x)u) = (1/2)(partial derivative(x)u)(2) has been derived, it has been shown through concrete examples that oscillations in v, v = partial derivative(x)u, in the initial data persist into positive time for the asymptotic equation. In the first part of this paper, we show by applying Young measure theory that no oscillations are generated if there are no oscillations (around a nonnegative state v) in the initial data, which implies in particular the global existence of weak solutions to the asymptotic equation with nonnegative L-p(R) initial data v with p > 2. In the second part, we obtain a regularity result for a large class of weak solutions to this equation by using its kinetic formulation. In particular this regularity result applies to both the conservative and dissipative weak solutions.
关键词	existence kinetic formulation regularity Young measure
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000078653300006
出版者	IOS PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13755
专题	中国科学院数学与系统科学研究院
作者单位	1.Chinese Acad Sci, Inst Math, Beijing 100080, Peoples R China 2.Indiana Univ, Dept Math, Bloomington, IN 47405 USA
推荐引用方式 GB/T 7714	Zhang, P,Zheng, YX. On oscillations of an asymptotic equation of a nonlinear variational wave equation[J]. ASYMPTOTIC ANALYSIS,1998,18(3-4):307-327.
APA	Zhang, P,&Zheng, YX.(1998).On oscillations of an asymptotic equation of a nonlinear variational wave equation.ASYMPTOTIC ANALYSIS,18(3-4),307-327.
MLA	Zhang, P,et al."On oscillations of an asymptotic equation of a nonlinear variational wave equation".ASYMPTOTIC ANALYSIS 18.3-4(1998):307-327.