In this paper, we give a sufficient conditions for the exact controllability of the non-linear generalized damped wave equation
on a Hilbert space. The distributed control and the operator is positive definite self-adjoint unbounded with compact resolvent. The non-linear term is a continuous function on and globally Lipschitz in the other variables. We prove that the linear system and the non-linear system are both exactly controllable; that is to say, the controllability of the linear system is preserved under the non-linear perturbation . As an application of this result one can prove the exact controllability of the Sine-Gordon equation.
Published May 30, 2005.
Math Subject Classifications: 34G10, 35B40.
Key Words: Non-linear generalized wave equations; strongly continuous groups; exact controllability; Sine-Gordon equation.
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| Hugo Leiva |
Department of Mathematics
Universidad de los Andes
Merida 5101, Venezuela
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