相关论文: Complex spherical waves and inverse problems in un…

Conductivity equation is studied in piecewise smooth plane domains and with measure-valued current patterns (Neumann boundary values). This allows one to extend the recently introduced concept of bisweep data to piecewise smooth domains,…

We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…

We prove boundary controllability results for wave equations (with lower-order terms) on Lorentzian manifolds with time-dependent geometry satisfying suitable curvature bounds. The main ingredient is a novel global Carleman estimate on…

The characterization problem of the existence of an unknown obstacle behind a known obstacle is considered by using a singe observed wave at a place where the wave is generated. The unknown obstacle is invisible from the place by using…

The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this…

In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…

We consider inverse problems for wave, heat and Schr\"odinger-type operators and corresponding spectral problems on domains of ${\bf R}^n$ and compact manifolds. Also, we study inverse problems where coefficients of partial differential…

The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…

We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial…

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…

Different practical problems, espesially, problems of hydrodynamics, elasticity theory, geophysics and aerodynamics can be reduced to finding of an optimal shape. The investigation of these problems is based on the study of depending domain…

We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…

Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schr\"odinger equation subject to periodic boundary conditions. When the circumference of the…

We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…

This paper is concerned with reconstruction issue of inverse obstacle problems governed by partial differential equations and consists of two parts. (i) The first part considers the foundation of the probe and enclosure methods for an…

We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…

We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally…

In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation,…