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Exact boundary and distributed controllability of radial damped wave equation. (English) Zbl 0910.93013
Several controllability results for the radial damped wave equations are presented. The damping terms appear both in the equation and in the boundary conditions. The results refer to the null controllability problem, to the closed loop control problem (i.e., the problem of finding a control such that the terminal state at a given time is a given multiple of its initial state) and to the periodic control problem. The control (function of time only) acts either as a forcing term in the right hand side of the equation or in the boundary conditions. The approach is based on several previous results of the author on the spectral analysis for the corresponding evolution operator, which is nonselfadjoint, in a suitable product space.
MSC:
93B05Controllability
93C20Control systems governed by PDE
93B28Operator-theoretic methods in systems theory