# Boundary and Distributed Controllability of the Damped Wave Equation: Reduction of Control Time

@article{Shubov1999BoundaryAD,
title={Boundary and Distributed Controllability of the Damped Wave Equation: Reduction of Control Time},
author={Marianna A. Shubov and Clyde F. Martin},
journal={Journal of Mathematical Analysis and Applications},
year={1999},
volume={240},
pages={16-36}
}
• Published 1 December 1999
• Mathematics
• Journal of Mathematical Analysis and Applications
Abstract We consider the zero controllability problem for the distributed parameter system governed by the damped wave equation u tt + 2d x u t − 1 ρ(x) d dx p(x) du dx + q x u = F x, t , where x ∈ [0, a], a  u x + ku t 0 = 0, u x + hu t a = ϕ t , h, k ∈ C ∪ ∞ . We consider two cases: (a) F(x, t) = g(x)f(t) and ϕ(t) is not identically zero; (b) ϕ(t) = 0 and F(x, t) = ∑mj = 1 g(j)(x)fj(t). The functions f(t), fj(t), and ϕ(t) are the distributed and boundary controls respectively. The problem…
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