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Controllability, returning waves and scattering without reverberation in 3D acoustic dynamic system
Mikhail I. Belishev, Aleksei F. Vakulenko
The dynamic acoustic scattering system is governed by the wave equation in , with a compactly supported potential and infinite…
On the M.Kac problem with augmented data
M. I. Belishev, A. F. Vakulenko
Let be a bounded plane domain. As is known, the spectrum of its Dirichlet Laplacian does not determine $Ω…
Non-smooth unobservable states in control problem for the wave equation in (corrected)
M. I. Belishev, A. F. Vakulenko
The paper deals with a dynamical system \begin{align*} &u_{tt}-Δu=0, \qquad (x,t) \in {\mathbb R}^3 \times (-\infty,0) \\ &u \mid_{|x|<-t} =0 , \qquad t<0\\ &\lim_{s \to \infty} su…
-points in acoustical scattering
Mikhail Belishev, Aleksei Vakulenko
The notion of -points has been introduced by the authors (SIAM JMA, 39 (2008), 1821--1850) in connection with the control problem for the dynamical system governed by the $3\rm…