Looking back on inverse scattering theory

D Colton, R Kress - SIAM Review, 2018 - SIAM
Looking Back on Inverse Scattering Theory Page 1 Copyright © by SIAM. Unauthorized
reproduction of this article is prohibited. SIAM REVIEW c 2018 Society for Industrial and Applied …

The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions

HM Nguyen, QH Nguyen - Journal of Functional Analysis, 2021 - Elsevier
The transmission problem is a system of two second-order elliptic equations of two
unknowns equipped with the Cauchy data on the boundary. After four decades of research …

The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions without complementing conditions

J Fornerod, HM Nguyen - SIAM Journal on Mathematical Analysis, 2023 - SIAM
The transmission eigenvalue problem is a system of two second-order elliptic equations of
two unknowns equipped with the Cauchy data on the boundary. In this work, we establish …

Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary

E Lakshtanov, A Lechleiter - SIAM Journal on Mathematical Analysis, 2016 - SIAM
We generalize the factorization method for inverse medium scattering using a particular
factorization of the difference of two far field operators. While the factorization method has …

Inside–outside duality with artificial backgrounds

L Audibert, L Chesnel, H Haddar - Inverse problems, 2019 - iopscience.iop.org
We use the inside–outside duality approach proposed by Kirsch–Lechleiter to identify
transmission eigenvalues (TEs) associated with artificial backgrounds. We prove that for well …

Solvability of interior transmission problem for the diffusion equation by constructing its Green function

G Nakamura, H Wang - Journal of Inverse and Ill-posed Problems, 2019 - degruyter.com
Consider the interior transmission problem arising in inverse boundary value problems for
the diffusion equation with discontinuous diffusion coefficients. We prove the unique …

[PDF][PDF] Exceptional points in Faddeev scattering problem

E Lakshtanov, B Vainberg - arxiv preprint arxiv:1407.1548, 2014 - Citeseer
Exceptional points are values of the spectral parameter for which the homogeneous
Faddeev scattering problem has a non-trivial solution. We show that these points coincide …

A factorization method and monotonicity bounds in inverse medium scattering for contrasts with fixed sign on the boundary

E Lakshtanov, A Lechleiter - arxiv preprint arxiv:1602.02883, 2016 - arxiv.org
We generalize the factorization method for inverse medium scattering using a particular
factorization of the difference of two far field operators. Whilst the factorization method been …

On the use of sampling methods and spectral signatures to identify defects in inhomogeneous media

K Napal - 2019 - theses.hal.science
This thesis is a contribution to inverse scattering theory. We are more specifically interested
in the non-destructive testing of heterogeneous materials such as composite materials by …

A test for the existence of exceptional points in the Faddeev scattering problem

EL Lakshtanov, BR Vainberg - Theoretical and Mathematical Physics, 2017 - Springer
Exceptional points are values of the spectral parameter for which the homogeneous
Faddeev scattering problem has a nontrivial solution. We formulate a criterion for existence …