• Corpus ID: 233864695

# Inverse wave scattering in the time domain for point scatterers

@inproceedings{Mantile2021InverseWS,
title={Inverse wave scattering in the time domain for point scatterers},
author={Andrea Mantile and Andrea Posilicano},
year={2021}
}
• Published 5 May 2021
• Mathematics
Abstract. Let ∆α,Y be the bounded from above self-adjoint realization in L (R) of the Laplacian with n point scatterers placed at Y = {y1, . . . , yn} ⊂ R, the parameters (α1, . . . αn) ≡ α ∈ R being related to the scattering properties of the obstacles. Let u fǫ and u∅fǫ denote the solutions of the wave equations corresponding to ∆α,Y and to the free Laplacian ∆ respectively, with a source term given by the pulse fǫ(x) = ∑N k=1 fk φǫ(x−xk) supported in ǫ-neighborhoods of the points in XN = {x1…

## References

SHOWING 1-10 OF 28 REFERENCES
Analysis of the Acoustic Waves Reflected by a Cluster of Small Holes in the Time-Domain and the Equivalent Mass Density
• Mathematics
Multiscale Model. Simul.
• 2021
We study the time-domain acoustic scattering problem by a cluster of small holes (i.e. sound-soft obstacles). Based on the retarded boundary integral equation method, we derive the asymptotic
Inverse wave scattering in the Laplace domain: A factorization method approach
• Mathematics
Proceedings of the American Mathematical Society
• 2020
Let $\Delta_{\Lambda}\le \lambda_{\Lambda}$ be a semi-bounded self-adjoint realization of the Laplace operator with boundary conditions (Dirichlet, Neumann, semi-transparent) assigned on the
Asymptotic completeness and S-matrix for singular perturbations
• Mathematics
Journal de Mathématiques Pures et Appliquées
• 2019
Direct and inverse time-harmonic elastic scattering from point-like and extended obstacles
• Mathematics
• 2019
This paper concerns the time-harmonic direct and inverse elastic scattering by an extended rigid elastic body surrounded by a finite number of point-like obstacles. We first justify the
Inverse scattering for the Laplace operator with boundary conditions on Lipschitz surfaces
• Mathematics
Inverse Problems
• 2019
We provide a general scheme, in the combined frameworks of Mathematical Scattering Theory and Factorization Method, for inverse scattering for the couple of self-adjoint operators
Limiting absorption principle, generalized eigenfunctions, and scattering matrix for Laplace operators with boundary conditions on hypersurfaces
• Mathematics
Journal of Spectral Theory
• 2018
We provide a limiting absorption principle for the self-adjoint realizations of Laplace operators corresponding to boundary conditions on (relatively open parts $\Sigma$ of) compact hypersurfaces
Direct and Inverse Acoustic Scattering by a Collection of Extended and Point-Like Scatterers
• Mathematics
Multiscale Model. Simul.
• 2014
It is shown that the scattered field is a sum of two contributions: one is due to the diffusion by the extended obstacle, and the other arises from the linear combination of the interactions between the point-like obstacles and the interaction with the extended one.
Inverse scattering by point-like scatterers in the Foldy regime
• Mathematics
• 2012
The scattering by point-like scatterers is described in the Born, Foldy and the intermediate regimes. We explain why the Foldy regime is, rigorously, a natural model for taking into account the
Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles
This article reviews Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles by P. A. Martin , 2006. 450 pp. Price: \$140.00 (hardcover). ISBN: 0-521-86554-9