Related papers: Stability estimates in stationary inverse transpor…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…
Following seminal work in the early 1980s that established the existence and representations of the homogenized transport coefficients for two phase random media, we develop a mathematical framework that provides Stieltjes integral…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…
We consider the stability of position control of traveling waves in reaction-diffusion system as proposed in {[}J. L\"ober, H. Engel, arXiv:1304.2327{]}. Instead of analyzing the controlled reaction-diffusion system, stability is studied on…
We follow up on work of Strauss, Weder, and Watanabe concerning scattering and inverse scattering for nonlinear Schr\"odinger equations with nonlinearities of the form $\alpha(x)|u|^p u$.
We show that fixed energy scattering measurements for the magnetic Schroedinger operator uniquely determine the magnetic field and electric potential in dimensions $n \geq 3$. The magnetic potential, its first derivatives, and the electric…
The problem of the recovery of a real-valued potential in the two-dimensional Schrodinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction…
We consider an inverse boundary value problem for the biharmonic operator with the first order perturbation in a bounded domain of dimension three or higher. Assuming that the first and the zeroth order perturbations are known in a…
We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal…
The contribution of this work is twofold. The first part deals with a Hilbert-space version of McCann's celebrated result on the existence and uniqueness of monotone measure-preserving maps: given two probability measures $\rm P$ and $\rm…
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…
We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. The measurements are made on the entirety of a smooth domain. Since tissues can be modeled as…
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…
This paper is devoted to the reconstruction of the time and space-dependent coefficient in an infinite cylindrical hyperbolic domain. Using a local Carleman estimate we prove the uniqueness and a H\"older stability in the determining of the…
In a medium where the dielectric permittivity is perturbed in the presence of an acoustic wave, optical scattering generates frequency-shifted light. In this paper we consider the inverse problem of recovering the optical properties of this…
For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach…
The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic, and electromagnetic media. In view of their promising applications in inverse problems related to…
Global stability of traveling wavefronts in a periodic spatial-temporal environment in $n$-dimension ($n\ge 1$) is studied. The wavefront is proved to be exponentially stable in the form of $ O(e^{-\mu t})$ for some $\mu>0$, when the wave…
We consider a periodic Jacobi operator $H$ with finitely supported perturbations on ${\Bbb Z}.$ We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data: the inverse of…