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| RAPID EXACT CONTROLLABILITY OF THE SEMILINEARWAVE EQUATION |
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Citation： |
ZHANG Xu.RAPID EXACT CONTROLLABILITY OF THE SEMILINEARWAVE EQUATION[J].Chinese Annals of Mathematics B,1999,20(3):378~384 |
| Page view： 1089
Net amount： 727 |
Authors： |
ZHANG Xu; |
Foundation： |
Science Foundation of the Ministry of
Education of China and the Youth
Science Foundation of
Shanghai's Universities |
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| Abstract： |
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. |
Keywords： |
Rapid exact controllability, Semilinear wave equation,
Changing controller,Energy estimate |
Classification： |
93B05, 35L05 |
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