Rarefactive solutions to a nonlinear variational wave equation of liquid crystals

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	Rarefactive solutions to a nonlinear variational wave equation of liquid crystals
	Zhang, P ; Zheng, YX
	2001
发表期刊	COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0360-5302
卷号	26 期号:3-4 页码:381-419
摘要	We study a nonlinear wave equation derived from a simplified liquid crystal model, in which the wave speed is a given function of the wave amplitude. We formulate a viscous approximation of the equation and establish the global existence of smooth solutions for the viscously perturbed equation. For a monotone wave speed function in the equation, we find an invariant region in the phase space in which we discover: (a) smooth data evolve smoothly forever; (b) both the viscous regularization and the smooth solutions obtained through data smoothing for rough initial data yield weak solutions to the Cauchy problem of the nonlinear variational wave equation. The main tool is the Young measure theory and related techniques.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000169918400002
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/16353
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, P
作者单位	1.Acad Sinica, 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. Rarefactive solutions to a nonlinear variational wave equation of liquid crystals[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,2001,26(3-4):381-419.
APA	Zhang, P,&Zheng, YX.(2001).Rarefactive solutions to a nonlinear variational wave equation of liquid crystals.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,26(3-4),381-419.
MLA	Zhang, P,et al."Rarefactive solutions to a nonlinear variational wave equation of liquid crystals".COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 26.3-4(2001):381-419.