| CHENG Jin,Masahiro YAMAMOTO,ZHOU Qi.[J].数学年刊A辑,1999,20(4):385~392 |
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| UNIQUE CONTINUATION ON A HYPERPLANE FORWAVE EQUATION |
| Received:May 17, 1999 |
| DOI： |
| 中文关键词: |
| 英文关键词:Unique continuation, Hyperplane, Wave operator,
Localized Fourier-Gauss,transform |
| 基金项目: |
| Author Name | Affiliation | E-mail | | CHENG Jin | Fudan University, Shanghai 200433, China | jcheng@fudan.edu.cn | | Masahiro YAMAMOTO | Graduate School of Mathematical Sciences,The University of Tokyo, Komaba 3-8-1, Meguro, Tokyo，153, Japan | myama@ms.u-tokyo.ac.jp | | ZHOU Qi | Graduate School of Mathematical Sciences,The University of Tokyo, Komaba 3-8-1, Meguro, Tokyo，153, Japan | qzhou@ms.u-tokyo.ac.jp |
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| 中文摘要: |
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| 英文摘要: |
| One kind of unique continuation property for a
wave equation is discussed. The authors show that, if one classical solution of the wave
equation vanishes in an open set on a hyperplane, then it must vanish in a
larger set on
this hyperplane. The result can be viewed as a localized version of
Robbiano's result$^{[9]}$. The approach involves the localized Fourier-Gauss
transformation and unique continuation on a line in the Laplace equation. |
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