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| Global Exact Boundary Controllability for Cubic Semi-linear Wave Equations and Klein-Gordon Equations |
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Citation： |
Yi ZHOU,Wei XU,Zhen LEI.Global Exact Boundary Controllability for Cubic Semi-linear Wave Equations and Klein-Gordon Equations[J].Chinese Annals of Mathematics B,2010,31(1):35~58 |
| Page view： 2117
Net amount： 1227 |
Authors： |
Yi ZHOU; Wei XU; Zhen LEI; |
Foundation： |
the National Natural Science Foundation of China (No. 10728101), the 973 Project of
the Ministry of Science and Technology of China, the Doctoral Program Foundation of the Ministry of Ed-
ucation of China, the “111” Project and the Postdoctoral Science Foundation of China (No. 20070410160). |
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| Abstract： |
The authors prove the global exact boundary controllability for the cubic semi-
linear wave equation in three space dimensions, subject to Dirichlet, Neumann, or any
other kind of boundary controls which result in the well-posedness of the corresponding
initial-boundary value problem. The exponential decay of energy is first established for the
cubic semi-linear wave equation with some boundary condition by the multiplier method,
which reduces the global exact boundary controllability problem to a local one. The proof
is carried out in line with [2, 15]. Then a constructive method that has been developed
in [13] is used to study the local problem. Especially when the region is star-complemented,
it is obtained that the control function only need to be applied on a relatively open subset
of the boundary. For the cubic Klein-Gordon equation, similar results of the global exact
boundary controllability are proved by such an idea. |
Keywords： |
Global exact boundary controllability, Cubic semi-linear wave equations,
The exponential decay, Star-shaped, Star-complemented, Cubic Klein-
Gordon equations |
Classification： |
35B37, 35L05 |
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