Looking back on inverse scattering theory
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 …
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
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 …
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 …
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 …
factorization of the difference of two far field operators. While the factorization method has …
Inside–outside duality with artificial backgrounds
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 …
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 …
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 …
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 …
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 …
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
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 …
Faddeev scattering problem has a nontrivial solution. We formulate a criterion for existence …