On oscillations of an asymptotic equation of a nonlinear variational wave equation
文献类型：期刊论文
| 作者 | Zhang, P; Zheng, YX |
| 刊名 | ASYMPTOTIC ANALYSIS
 |
| 出版日期 | 1998-12-01 |
| 卷号 | 18期号:3-4页码:307-327 |
| 关键词 | existence kinetic formulation regularity Young measure |
| ISSN号 | 0921-7134 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000078653300006 |
| 出版者 | IOS PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/13754]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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