Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Katsnelson, Vitaly"'
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 a gas or liquid between the unperturbed and perturbed flow is denoted
Externí odkaz:
http://arxiv.org/abs/2410.06360
We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in between the i
Externí odkaz:
http://arxiv.org/abs/2302.14158
We consider an isotropic elastic medium occupying a bounded domain D whose density and Lam\'e parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but on
Externí odkaz:
http://arxiv.org/abs/2203.08735
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 (exploration) seismology in this context. However, the analysis in seismology ha
Externí odkaz:
http://arxiv.org/abs/2201.02607
Consider an isotropic elastic medium $\Omega \subset \mathbb{R}^3$ whose Lam\'e parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but only outside $\O
Externí odkaz:
http://arxiv.org/abs/1903.05553
Let $c$ be a piecewise smooth wave speed on $\mathbb R^n$, unknown inside a domain $\Omega$. We are given the solution operator for the scalar wave equation $(\partial_t^2-c^2\Delta)u=0$, but only outside $\Omega$ and only for initial data supported
Externí odkaz:
http://arxiv.org/abs/1801.03144
Publikováno v:
In Journal de mathématiques pures et appliquées April 2022 160:54-98
Autor:
Katsnelson, Vitaly, Nguyen, Linh V.
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 Problems 28.5 (2012): 055004], converges with the sharp observation t
Externí odkaz:
http://arxiv.org/abs/1707.05822
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 at the length spectrum of periodic broken rays. In particular, the Neum
Externí odkaz:
http://arxiv.org/abs/1705.10434
Consider the acoustic wave equation with unknown, not necessarily smooth, wave speed $c$. We propose and study an iterative control procedure that erases the history of a wave field up to a given depth in a medium, without any knowledge of $c$. In th
Externí odkaz:
http://arxiv.org/abs/1701.01070