Exact Distributed Controllability for The Semilinear Wave Equation

Wei-Jiu Liu

Abstract: In this paper we generalize the theorems of exact controllability for the linear wave equation with a distributed control to the semilinear case, showing that, given $T$ large enough, for every initial state in a sufficiently small neighbourhood of the origin in a certain function space, there exists a distributed control, supported on a part of a domain, driving the system to rest. Also, if the control is allowed to support on the entire domain, then we prove that the system is globally exactly controllable at any time $T$.

Keywords: Distributed controllability; semilinear wave equation.

Classification (MSC2000): 93B05, 35B37, 35L05.

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