24,689 research outputs found
Stability estimates for an inverse scattering problem at high frequencies
We consider an inverse scattering problem and its near-field approximation at
high frequencies. We first prove, for both problems, Lipschitz stability
results for determining the low-frequency component of the potential. Then we
show that, in the case of a radial potential supported sufficiently near the
boundary, infinite resolution can be achieved from measurements of the
near-field operator in the monotone case
Stable determination of a scattered wave from its far-field pattern: the high frequency asymptotics
We deal with the stability issue for the determination of outgoing
time-harmonic acoustic waves from their far-field patterns. We are especially
interested in keeping as explicit as possible the dependence of our stability
estimates on the wavenumber of the corresponding Helmholtz equation and in
understanding the high wavenumber, that is frequency, asymptotics.
Applications include stability results for the determination from far-field
data of solutions of direct scattering problems with sound-soft obstacles and
an instability analysis for the corresponding inverse obstacle problem.
The key tool consists of establishing precise estimates on the behavior of
Hankel functions with large argument or order.Comment: 49 page
Inverse boundary value problem for the Helmholtz equation: quantitative conditional Lipschitz stability estimates
We study the inverse boundary value problem for the Helmholtz equation using
the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional
Lipschitz stability estimate for the inverse problem holds in the case of
wavespeeds that are a linear combination of piecewise constant functions
(following a domain partition) and gives a framework in which the scheme
converges. The stability constant grows exponentially as the number of
subdomains in the domain partition increases. We establish an order optimal
upper bound for the stability constant. We eventually realize computational
experiments to demonstrate the stability constant evolution for three
dimensional wavespeed reconstruction.Comment: 21 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1406.239
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