相关论文: Inverse Scattering for the Laplace operator with b…
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…
We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across $\Sigma\subseteq\Gamma=\partial\Omega$, where $\Omega$ is a bounded open subset of $\mathbb{R}^{3}$ with a Lipschitz…
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 $\Gamma=\partial\Omega$,…
We describe inverse scattering for the matrix Schroedinger operator with general selfadjoint boundary conditions at the origin using the Marchenko equation. Our approach allows the recovery of the potential as well as the boundary…
We provide an asymptotic completeness criterion and a representation formula for the scattering matrix of the scattering couple $(A_B,A)$, where both $A$ and $A_B$ are self-adjoint operator and $A_B$ formally corresponds to adding to $A$…
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…
We prove a fixed frequency inverse scattering result for the magnetic Schr\"odinger operator (or connection Laplacian) on surfaces with Euclidean ends. We show that, under suitable decaying conditions, the scattering matrix for the operator…
We investigate the Bi-Laplacian with Wentzell boundary conditions in a bounded domain $\Omega\subseteq\mathbb{R}^d$ with Lipschitz boundary $\Gamma$. More precisely, using form methods, we show that the associated operator on the ground…
The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…
In this paper the spectral and scattering properties of a family of self-adjoint Dirac operators in $L^2(\Omega; \mathbb{C}^4)$, where $\Omega \subset \mathbb{R}^3$ is either a bounded or an unbounded domain with a compact $C^2$-smooth…
The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…
This paper analyzes the scattering matrix for two unbounded self-adjoint operators: the standard Laplace operator in three-dimensional space and a second operator that differs from the first by an infinite sum of zero-range potentials.
In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second…
It is proved that the scattering amplitude $A(\beta, \alpha_0, k_0)$, known for all $\beta\in S^2$, where $S^2$ is the unit sphere in $\mathbb{R}^3$, and fixed $\alpha_0\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the…
Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…
We present a solution to the inverse scattering problem for differential Laplace operators on metric noncompact graphs. We prove that for almost all boundary conditions (i) the scattering matrix uniquely determines the graph and its metric…
The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic operator on $\mathbb{R}^{n}$ with linear boundary conditions on (a relatively open part of) a…
Applying the inverse scattering transform to study a focusing two-component Hirota equation with nonzero boundary conditions at infinity. Through the spectral problem and the adjoint spectral problem, the analyticity properties and symmetry…
It is proved that the scattering amplitude $A(\beta, \alpha_0, k_0)$, known for all $\beta\in S^2$, where $S^2$ is the unit sphere in $\mathbb{R}^3$, and fixed $\alpha_0\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…