2,140 research outputs found
Recovery of time-dependent damping coefficients and potentials appearing in wave equations from partial data
We consider the inverse problem of determining a time-dependent damping
coefficient and a time-dependent potential , appearing in the wave
equation in
, with and a bounded domain
of , , from partial observations of the solutions on
. More precisely, we look for observations on that
allow to determine uniquely a large class of time-dependent damping
coefficients and time-dependent potentials without involving an
important set of data. We prove global unique determination of , with , and from partial observations on
Determination of singular time-dependent coefficients for wave equations from full and partial data
We study the problem of determining uniquely a time-dependent singular
potential , appearing in the wave equation in with and a
bounded domain of , . We start by considering the unique
determination of some singular time-dependent coefficients from observations on
. Then, by weakening the singularities of the set of admissible
coefficients, we manage to reduce the set of data that still guaranties unique
recovery of such a coefficient. To our best knowledge, this paper is the first
claiming unique determination of unbounded time-dependent coefficients, which
is motivated by the problem of determining general nonlinear terms appearing in
nonlinear wave equations
Stability in the determination of a time-dependent coefficient for wave equations from partial data
We consider the stability in the inverse problem consisting of the
determination of a time-dependent coefficient of order zero , appearing in a
Dirichlet initial-boundary value problem for a wave equation
in with a
bounded domain of , , from partial observations on
. The observation is given by a boundary operator associated to the
wave equation. Using suitable complex geometric optics solutions and Carleman
estimates, we prove a stability estimate in the determination of from the
boundary operator
Partial data inverse problem for hyperbolic equation with time-dependent damping coefficient and potential
We study an inverse problem of determining time-dependent damping coefficient
and potential appearing in the wave equation in a compact Riemannian manifold
of dimension three or higher. More specifically, we are concerned with the case
of conformally transversally anisotropic manifolds, or in other words, compact
Riemannian manifolds with boundary conformally embedded in a product of the
Euclidean line and a transversal manifold. With an additional assumption of the
attenuated geodesic ray transform being injective on the transversal manifold,
we prove that the knowledge of a certain partial Cauchy data set determines
time-dependent damping coefficient and potential uniquely.Comment: arXiv admin note: text overlap with arXiv:1702.07974 by other author
Stability estimate in an inverse problem for non-autonomous Schr\"odinger equations
We consider the inverse problem of determining the time dependent magnetic
field of the Schr\"odinger equation in a bounded open subset of , with , from a finite number of Neumann data, when the boundary measurement is
taken on an appropriate open subset of the boundary. We prove the Lispchitz
stability of the magnetic potential in the Coulomb gauge class by times
changing initial value suitably
- …