28 citations · 93 across the 40 of their papers we have counts for
22 papers · 1 filter
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…
N-transform and factorization of the DN-map
M. I. Belishev, D. V. Korikov
Let be a smooth compact 3D Riemannian manifold with the smooth boundary , , ; \}, $Γ^τ:=\{x\inΩ\,…
On a stability of time-optimal version of the Boundary Control method
Mikhail I. Belishev
Let be a Riemannian manifold with boundary. The time-optimal version of the BC-method determines the parameters in the -neigh\-bor\-hood of from the bounda…
Functional models and self-modeling property of minimal Dirac operators on the half-line
M. I. Belishev, S. A. Simonov
We prove that minimal Dirac operators on the half-line are self-modeling, which means that such an operator is determined by its arbitrary unitary copy uniquely up to a transformat…
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…
Triangular factorization of operators and reconstruction of systems
M. I. Belishev
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme…
A functional model of a class of symmetric semi-bounded operators
M. I. Belishev, S. A. Simonov
Let be a closed symmetric positive definite operator with nonzero defect indices in a separable Hilbert space . It determines a family of dynamical…
Canonical forms of metric graph eikonal algebra and graph geometry
M. I. Belishev, A. V. Kaplun
The algebra of eikonals of a metric graph is an operator -algebra determined by dynamical system with boundary control that describes wave propagation on the…
Stability of determination of Riemann surface from its DN-map in terms of Teichmüller distance
M. I. Belishev, D. V. Korikov
As is known, the Dirichlet-to-Neumann operator of a Riemannian surface determines the surface up to conformal equivalence class . Such classes constitute the T…
On stability of determination of Riemann surface from its DN-map
M. I. Belishev, D. V. Korikov
Suppose that is a Riemann surface with boundary , is its DN-map, and % is a holomorphic immersion. Let b…
Electric Impedance Tomography problem for surfaces with internal holes
A. V. Badanin, M. I. Belishev, D. V. Korikov
Let be a smooth compact Riemann surface with the multicomponent boundary . Let obey in , $u|_{Γ_0}=f,\,\,u|_…
On the EIT problem for nonorientable surfaces
M. I. Belishev, D. V. Korikov
Let be a smooth compact two-dimensional Riemannian manifold with boundary, its DN map, where obeys in and $u|_{\p…
Data characterization in dynamical inverse problem for the 1d wave equation with matrix potential
Mikhail Belishev, Timur Khabibullin
The dynamical system under consideration is \begin{align*} & u_{tt}-u_{xx}+Vu=0,\qquad x>0,\,\,\,t>0;\\ & u|_{t=0}=u_t|_{t=0}=0,\,\,x\geqslant 0;\quad u|_{x=0}=f,\,\,t\geqslant 0,…
Eikonal algebra on a graph of simple structure
M. I. Belishev, A. V. Kaplun
An eikonal algebra is a C*-algebra related to a metric graph . It is determined by trajectories and reachable sets of a dynamical system associated with the g…
Local boundary controllability in classes of differentiable functions for the wave equation
M. I. Belishev
The well-known fact following from the Holmgren-John-Tataru uniqueness theorem is a local approximate boundary -controllability of the dynamical system governed by the wave eq…
On algebras of three-dimensional quaternionic harmonic fields
M. I. Belishev
A quaternionic field is a pair of function and vector field given on a 3d Riemannian maifold with the boundary. The field is said to be harmonic if $\nabla…
On a calculus of variations problem
Mikhail I. Belishev, Aleksandr V. Ivanov
The paper is of scientific-methodical character. The classical soap film shape (minimal surface) problem is considered, the film being stretched between two parallel coaxial rings.…
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…
A C*-algebra associated with dynamics on a graph of strings
M. I. Belishev, N. Wada
A C*-algebra associated with a dynamical system on a metric graph is introduced. The system is governed by the wave equation and controlled from boundary vertices. Al…
Elements of noncommutative geometry in inverse problems on manifolds
M. I. Belishev, M. N. Demchenko
We deal with two dynamical systems associated with a Riemannian manifold with boundary. The first one is a system governed by the scalar wave equation, the second is governed by th…
C*-algebras and inverse problem of electrodynamics
M. I. Belishev, M. N. Demchenko
We consider the dynamical inverse problem for the Maxwell system on a Riemannian 3-manifold with boundary in a time-optimal set-up. Using BC-method we show that the data of the inv…
-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…