Bilinear controllability properties of a vibrating string with variable axial load and damping gain. (English) Zbl 1035.35015

Khapalov, A. Y.

Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 10, No. 5, 721-743 (2003).

The initial and boundary value problem for the one dimensional wave equation modeling oscillations of a damped vibrating string with clapped ends and an axial load is considered. It is shown that the set of equilibrium states like \((y_{d},0)\) of a vibrating string that can approximately be reached in \(H_{0}^{1}(0,1)\times L^{2}(0,1)\) by varying its axial load, and the gain of damping is dense in the subspace \(H_{0}^{1}(0,1)\times \{0\}\) of this space.

Reviewer: Gheorghe Aniculăesei (Iaşi)

MSC:

35B37	PDE in connection with control problems (MSC2000)
93B05	Controllability
35L05	Wave equation
35L20	Initial-boundary value problems for second-order hyperbolic equations

Keywords:

gain of damping is dense