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Exact controllability for the semilinear string equation in non cylindrical domains

Araruna F. D., Antunes G. O., Medeiros L. A.

Control and Cybernetics

2004

Vol. 33, no 2

237-257

In this paper, we investigate the exact controllability for a mixed problem for the equation u^n - [...] + f(u) = 0 in a non cylindrical domain. This model, without the resistance represented for f(u), is a linearization of Kirchhoff's equation for small vibrations of a stretched elastic string when the ends are variables, see Medeiros, Limaco, Menezes (2002). We employ a variant, due to Zuazua (1990b), of the Hilbert Uniqueness Method (HUM), idealized by Lions (1988a, b).