Explicit observability estimate for the wave equation with potential and its application

By means of the Carleman-type estimate, we obtain an explicit observability estimate for the wave equation with a potential. As its application, we get the exact internal controllability of the semilinear wave equations in any space dimensions.

[1]  M. S. Baouendi,et al.  A non uniqueness result for operators of principal type , 1995 .

[2]  Lop Fat Ho Observabilité frontière de l'équation des ondes , 1986 .

[3]  Jacques-Louis Lions Contrôlabilite exacte et homogénéisation (I) , 1988 .

[4]  D. Tataru,et al.  Boundary controllability for conservative PDEs , 1995 .

[5]  Kangsheng Liu Locally Distributed Control and Damping for the Conservative Systems , 1997 .

[6]  R. Triggiani,et al.  Exact controllability for second-order hyperbolic equations with variable coefficient-principal part and first-order terms , 1997 .

[7]  V. Komornik Exact Controllability and Stabilization: The Multiplier Method , 1995 .

[8]  D. Russell Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions , 1978 .

[9]  Irena Lasiecka,et al.  Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems , 1989 .

[10]  Oleg Yu. Imanuvilov,et al.  Controllability of Evolution equations , 1996 .

[11]  Enrique Zuazua,et al.  Exact controllability for semilinear wave equations in one space dimension , 1993 .

[12]  C. Bardos,et al.  Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary , 1992 .

[13]  M. M. Lavrentʹev,et al.  Ill-Posed Problems of Mathematical Physics and Analysis , 1986 .

[14]  Michael V. Klibanov,et al.  Stability estimates for ill-posed Cauchy problems involving hyperbolic equations and inequalities , 1993 .