Inverse wave scattering in the Laplace domain: A factorization method approach

@article{Mantile2020InverseWS,
  title={Inverse wave scattering in the Laplace domain: A factorization method approach},
  author={Andrea Mantile and Andrea Posilicano},
  journal={Proceedings of the American Mathematical Society},
  year={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 Lipschitz boundary of a bounded obstacle $\Omega$. Let $u^{\Lambda}_{f}$ and $u^{0}_{f}$ denote the solutions of the wave equations corresponding to $\Delta_{\Lambda}$ and to the free Laplacian $\Delta$ respectively, with a source term $f$ concentrated at time $t=0$ (a pulse). We show that for any fixed… 
1 Citations
Inverse wave scattering in the time domain for point scatterers
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

References

SHOWING 1-10 OF 31 REFERENCES
Inverse scattering for the Laplace operator with boundary conditions on Lipschitz surfaces
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
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
Asymptotic completeness and S-matrix for singular perturbations
On inverses of Krein's Q-functions
Let $A_{Q}$ be the self-adjoint operator defined by the $Q$-function $Q:z\mapsto Q_{z}$ through the Krein-like resolvent formula $$(-A_{Q}+z)^{-1}= (-A_{0}+z)^{-1}+G_{z}WQ_{z}^{-1}VG_{\bar
A sampling method for inverse scattering in the time domain
We consider a near-field inverse scattering problem for the wave equation: find the shape of a Dirichlet scattering object from time domain measurements of scattered waves. For this time-domain
An improved time domain linear sampling method for Robin and Neumann obstacles
We consider inverse obstacle scattering problems for the wave equation with Robin or Neumann boundary conditions. The problem of reconstructing the geometry of such obstacles from measurements of
A Krein-like Formula for Singular Perturbations of Self-Adjoint Operators and Applications
Abstract Given a self-adjoint operator A :  D ( A )⊆ H → H and a continuous linear operator τ :  D ( A )→ X with Range τ ′∩ H ′={0}, X a Banach space, we explicitly construct a family A τ Θ of
The point source method for inverse scattering in the time domain
Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency
Parameter identification for Maxwell's equations
In this work we present a variational algorithm to determine the parameters iir(x) and er(x) in the Maxwell system VxE + k xTH = 0, V x H - kerE = 0 in a body Q from boundary measurements of
...
...