Related papers: Reconstruction and stability for piecewise smooth …

In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We…

We give formulas and equations for finding generalized scattering data for the Schr\"odinger equation in open bounded domain at fixed energy from the impedance boundary map (or Robin-to-Robin map). Combining these results with results of…

The aim of this paper is to study the recovery of a spatially dependent potential in a (sub)diffusion equation from overposed final time data. We construct a monotone operator one of whose fixed points is the unknown potential. The…

We consider the problem to reconstruct a wave speed $c \in C^\infty(M)$ in a domain $M \subset \R^n$ from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction formula…

We prove stability estimates for the problem of recovering the nonlinearity from scattering data. We focus our attention on nonlinear Schr\"odinger equations of the form \[ (i\partial_t+\Delta)u = a(x)|u|^p u \] in three space dimensions,…

A new stable computational method for non-homogeneous waveguide equation with a piecewise uniform structure along the main propagation direction is constructed, based on the modified Dirichlet-to-Neumann (DtN) map of each uniform segment.…

In this paper we consider the unique determination of inhomogeneities together with possible buried obstacles by scattering measurements. Under the assumption that the buried obstacles have only planar contacts with the inhomogeneities, we…

We consider the problem of reconstructing of the boundary of an unknown inclusion together with its conductivity from the localized Dirichlet-to-Neumann map. We give an exact reconstruction procedure and apply the method to an inverse…

In this paper, we prove the uniform stability of the Hochstadt-Lieberman problem, which consists in the recovery of the Sturm-Liouville potential on a half-interval from the spectrum and the known potential on the other half-interval. For…

We consider the unique recovery of a non compactly supported and non periodic perturbation of a Schr\"odinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery…

We establish a triple logarithmic stability estimate of determining the potential in a Helmholtz equation from a partial Dirichlet-to-Neumann map in the high frequency limit. This estimate is proved under the assumption that the potential…

We show the validity of Nachman's procedure (Ann. Math. 128(3):531-576, 1988) for reconstructing a conductivity function $\gamma$ in a smooth bounded domain $\Omega \subset \mathbb{R}^n$ ($n\geq 3$) from its Dirichlet-to-Neumann map…

Accurate reconstruction of piecewise-smooth functions from a finite number of Fourier coefficients is an important problem in various applications. The inherent inaccuracy, in particular the Gibbs phenomenon, is being intensively…

We revisit the stability issue of determining the conductivity at the boundary from the corresponding Dirichlet-to-Neumann map. We discuss both the method based on singular solutions and the one built on the localized oscillating solutions.…

We develop the d-bar approach to inverse scattering at fixed energy in dimensions $d\ge 3$ of [Beals, Coifman 1985] and [Henkin, Novikov 1987]. As a result we propose a stable method for nonlinear approximate finding a potential $v$ from…

This paper concerns an inverse boundary value problem of recovering a zeroth order time-dependent term of a semi-linear wave equation on a globally hyperbolic Lorentzian manifold. We show that an unknown potential $q$ in the non-linear wave…

We prove that a potential $q$ can be reconstructed from the Dirichlet-to-Neumann map for the Schrodinger operator $-\Delta_g + q$ in a fixed admissible 3-dimensional Riemannian manifold $(M,g)$. We also show that an admissible metric $g$ in…

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…

The probe method gives a general idea to obtain a reconstruction formula of unknown objects embedded in a known background medium from a mathematical counterpart (the Dirichlet-to-Neumann map) of the measured data of some physical quantity…

In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and…