
Leonid PestovImmanuel Kant Baltic Federal University | IKSUR
Leonid Pestov
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9
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Publications
Publications (9)
We consider initial boundary-value problem for acoustic equation in the time space cylinder Ω × (0; 2T) with unknown variable speed of sound, zero initial data, and mixed boundary conditions. We assume that (Neumann) controls are located at some part Σ Ω [0; T]; Σ ⊂ 𝜕Ω of the lateral surface of the cylinder Ω × (0; T). The domain of observation is...
Given a bounded domain M in R n > with a conformally Euclidean metric g = &rgr; dx 2 > , we consider the inverse problem of recovering a semigeodesic neighborhood of a domain Γ ⊂ ∂ M > and the conformal factor ρ in the neighborhood from the travel time data (defined below) and the Cartesian coordinates of Γ. We develop an explicit reconstruction pr...
We develop the numerical algorithm for solving the inverse problem for
the wave equation by the Boundary Control method. The problem, which we
refer to as a forward one, is an initial boundary value problem for the
wave equation with zero initial data in the bounded domain. The inverse
problem is to find the speed of sound c(x) by the measurements...
In this paper we develop numerical algorithm for solving inverse problem for the wave equation using Boundary Control method. The results of numerical experiments are represented.
We outline the proof that two dimensional simple Riemannian man-ifolds with boundary are boundary distance rigid. In addition we give, in two dimensions, a reconstruction procedure to recover the index of refraction of a bounded medium in Euclidean space from the travel times of sound waves going through the medium.
We describe a relation between the scattering relation, the Hilbert transform in frequency space, and the geodesic ray transform for simple, two-dimensional compact Riemannian manifolds with boundary. We use this relation to give a characterization of the range of the geodesic X-ray transform acting on scalar functions and vector fields in terms of...
We prove that knowing the lengths of geodesics joining points of the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction.