KMS Of Academy of mathematics and systems sciences, CAS
| Rarefactive solutions to a nonlinear variational wave equation of liquid crystals | |
| Zhang, P; Zheng, YX | |
| 2001 | |
| Source Publication | COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
 |
| ISSN | 0360-5302 |
| Volume | 26Issue:3-4Pages:381-419 |
| Abstract | 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. |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000169918400002 |
| Publisher | MARCEL DEKKER INC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/16353 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Zhang, P |
| Affiliation | 1.Acad Sinica, Inst Math, Beijing 100080, Peoples R China 2.Indiana Univ, Dept Math, Bloomington, IN 47405 USA |
| Recommended Citation 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. |
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