2003 Colloquium on Differential Equations and Applications,
Maracaibo, Venezuela.
Electron. J. Diff. Eqns., Conference 13, 2005, pp. 7588.
Exact controllability of a nonlinear generalized damped
wave equation: Application to the SineGordon equation
Hugo Leiva
Abstract:
In this paper, we give a sufficient conditions for the exact
controllability of the nonlinear generalized damped
wave equation
on a Hilbert space. The distributed control
and the
operator
is positive definite selfadjoint unbounded with
compact resolvent. The nonlinear term
is a continuous
function on
and globally Lipschitz in the other variables.
We prove that the linear system and the nonlinear system are both
exactly controllable; that is to say, the controllability of
the linear system is preserved under the nonlinear perturbation
.
As an application of this result one can prove the exact controllability
of the SineGordon equation.
Published May 30, 2005.
Math Subject Classifications: 34G10, 35B40.
Key Words: Nonlinear generalized wave equations;
strongly continuous groups; exact controllability;
SineGordon equation.
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Hugo Leiva
Department of Mathematics
Universidad de los Andes
Merida 5101, Venezuela
email: hleiva@ula.ve

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