| ZHANG Xu.[J].数学年刊A辑,1999,20(3):378~384 |
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| RAPID EXACT CONTROLLABILITY OF THE SEMILINEARWAVE EQUATION |
| Received:June 17, 1997 Revised:October 30, 1998 |
| DOI： |
| 中文关键词: |
| 英文关键词:Rapid exact controllability, Semilinear wave equation,
Changing controller,Energy estimate |
| 基金项目: |
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| 中文摘要: |
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| 英文摘要: |
| In this paper the semilinear wave equation with
homogeneous Dirichlet boundary condition having a locally distributed
controller is considered, and
the rapid exact controllability of this system is obtained by changing the shape and/or
the location of the controller under proper conditions. For this purpose,
the author derives an (rapid) observability inequality for wave equations with
linear time-variant potential by means of the energy estimate. The main difference
of the method from the previous ones is that any unique continuation property
of the corresponding linear time-variant wave equations is not needed. |
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