14 citations · 31 across the 10 of their papers we have counts for
12 papers
Principal spectral rigidity implies subprincipal spectral rigidity
Maarten V. de Hoop, Joonas Ilmavirta, Vitaly Katsnelson
We study the inverse spectral problem of jointly recovering a radially symmetric Riemannian metric and an additional coefficient from the Dirichlet spectrum of a perturbed Laplace-…
Recovery of piecewise smooth parameters in an acoustic-gravitational system of equations from exterior Cauchy data
Sombuddha Bhattacharyya, Maarten de Hoop, Vitaly Katsnelson
In this paper, we study an inverse problem for an acoustic-gravitational system whose principal symbol is identical to that of an acoustic wave operator. The displacement vector of…
Spherically symmetric terrestrial planets with discontinuities are spectrally rigid
Joonas Ilmavirta, Maarten V. de Hoop, Vitaly Katsnelson
We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rathe…
Recovery of piecewise smooth density and Lamé parameters from high-frequency exterior Cauchy data
Sombuddha Bhattacharyya, Maarten V. de Hoop, Vitaly Katsnelson +1
We consider an isotropic elastic medium occupying a bounded domain D whose density and Lamé parameters are piecewise smooth. In the elastic wave initial value inverse problem, we a…
Recovery of wave speeds and density of mass across a heterogeneous smooth interface from acoustic and elastic wave reflection operators
Sombuddha Bhattacharyya, Maarten V. de Hoop, Vitaly Katsnelson +1
We revisit the problem of recovering wave speeds and density across a curved interface from reflected wave amplitudes. Such amplitudes have been exploited for decades in (explorati…
Recovery of discontinuous Lamé parameters from local dynamic boundary data
Peter Caday, Maarten V. de Hoop, Vitaly Katsnelson +1
Consider an isotropic elastic medium whose Lamé parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solutio…
Reconstruction of piecewise smooth wave speeds using multiple scattering
Peter Caday, Maarten V. de Hoop, Vitaly Katsnelson +1
Let be a piecewise smooth wave speed on , unknown inside a domain . We are given the solution operator for the scalar wave equation , bu…
Time reversal method for thermoacoustic acoustic tomography in elastic media: convergence with sharp observation time
Vitaly Katsnelson, Linh V. Nguyen
In this article, we consider the inverse source problem arising in photoacoustic tomography in elastic media. We show that the time reversal method, proposed by Tittelfitz [Inverse…
Spectral rigidity for spherically symmetric manifolds with boundary
Maarten V. de Hoop, Joonas Ilmavirta, Vitaly Katsnelson
We prove a trace formula for three-dimensional spherically symmetric Riemannian manifolds with boundary which satisfy the Herglotz condition: The wave trace is singular precisely a…
Scattering Control for the Wave Equation with Unknown Wave Speed
Peter Caday, Maarten V. de Hoop, Vitaly Katsnelson +1
Consider the acoustic wave equation with unknown, not necessarily smooth, wave speed . We propose and study an iterative control procedure that erases the history of a wave fiel…
Diffraction of Elastic Waves by Edges
Vitaly Katsnelson
We investigate the diffraction of singularities of solutions to the linear elastic equation on manifolds with edge singularities. Such manifolds are modeled on the product of a smo…
Sign patterns for chemical reaction networks
J. William Helton, Igor Klep, Vitaly Katsnelson
Most differential equations found in chemical reaction networks (CRNs) have the form , where lies in the nonnegative orthant, where is a real matrix (the…