28 citations · 93 across the 40 of their papers we have counts for
39 papers
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 stability of triangular factorization of positive operators
M. I. Belishev, A. F. Vakulenko
Let be a nest and a bounded positive operator in a Hilbert space . The representation provided $V\mathscr F_s\subset\m…
Unified approach to classical equations of inverse problem theory
M. I. Belishev, V. S. Mikhaylov
The boundary control (BC-) method is an approach to inverse problems based upon their deep relations to control and system theory. We show that the classical integral equations of…
On an inverse problem in photoacoustic
M. I. Belishev, D. Langemann, A. S. Mikhaylov +1
We consider the problem of reconstruction of the Cauchy data for the wave equation in and by the measurements of its solution on the boundary of the u…
Inverse problem for one-dimensional dynamical Dirac system (BC-method)
Mikhail Belishev, Victor Mikhailov
A forward problem for the Dirac system is to find obeying $iu_t+\begin{pmatrix}0&1\\-1&0\end{pmatrix}u_x+\begin{pmatrix}p&q\\q&-p…
Comment on the preprint arXiv:2501.17471 "Two-dimensional Calderon Problem and Flat Metrics" by V.A.Sharafutdinov
M. I. Belishev
The notice provides some critical remarks on a paper (preprint) by V.A.Sharafutdinov. The remarks mainly concern Theorem 1.1 on determination of the Riemann surface from its Dirich…
Three-dimensional inverse acoustic scattering problem by the BC-method
M. I. Belishev, A. F. Vakulenko
Let , . The {\it forward} acoustic scattering problem under consideration is to find satisfying \begin{align} \label{Eq 01…
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…
Wave propagation in abstract dynamical system with boundary control
M. I. Belishev
Let be a positive definite operator in a Hilbert space with the defect indexes and let be its canonical (by M.I…
Canonical form of -algebra of eikonals related to the metric graph
M. I. Belishev, A. V. Kaplun
The eikonal algebra of the metric graph is an operator --algebra defined by the dynamical system which describes the propagation of waves generated by source…
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…
Toeplitz matrices in the Boundary Control method
M. I. Belishev, N. A. Karazeeva
Solving inverse problems by dynamical variant of the BC-method is basically reduced to inverting the connecting operator of the dynamical system, for which the problem is sta…
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 characterization of Dirichlet-to-Neumann map of Riemannian surface with boundary
M. I. Belishev, D. V. Korikov
Let be a smooth compact orientable two-dimensional Riemannian manifold ({\it surface}) with a smooth metric tensor and smooth connected boundary . Its {\it DN-map} $…
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…