205 research outputs found
Lipschitz stability of an inverse boundary value problem for a Schr\"{o}dinger type equation
In this paper we study the inverse boundary value problem of determining the
potential in the Schr\"{o}dinger equation from the knowledge of the
Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in
the sense that, under general settings, the optimal stability estimate is of
logarithmic type. In this work, a Lipschitz type stability is established
assuming a priori that the potential is piecewise constant with a bounded known
number of unknown values
Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities
We discuss the inverse problem of determining the, possibly anisotropic,
conductivity of a body when the so-called
Neumann-to-Dirichlet map is locally given on a non empty curved portion
of the boundary . We prove that anisotropic
conductivities that are \textit{a-priori} known to be piecewise constant
matrices on a given partition of with curved interfaces can be
uniquely determined in the interior from the knowledge of the local
Neumann-to-Dirichlet map
Reconstruction of Lame moduli and density at the boundary enabling directional elastic wavefield decomposition
We consider the inverse boundary value problem for the system of equations
describing elastic waves in isotropic media on a bounded domain in
via a finite-time Laplace transform. The data is the dynamical
Dirichlet-to-Neumann map. More precisely, using the full symbol of the
transformed Dirichlet-to-Neumann map viewed as a semiclassical
pseudodifferential operator, we give an explicit reconstruction of both
Lam\'{e} parameters and the density, as well as their derivatives, at the
boundary. We also show how this boundary reconstruction leads to a
decomposition of incoming and outgoing waves
Uniqueness for a seismic inverse source problem modeling a subsonic rupture
We consider an inverse problem for an inhomogeneous wave equation with
discrete-in-time sources, modeling a seismic rupture. We assume that the
sources occur along a path with subsonic velocity, and that data are collected
over time on some detection surface. We explore the question of uniqueness for
these problems, show how to recover the times and locations of sources
microlocally, and then reconstruct the smooth part of the source assuming that
it is the same at each source location
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