相关论文: Examples of nonuniqueness for an inverse problems …
Identifying earth pressures on in-service transportation tunnel linings is essential for their health monitoring and performance prediction, particularly in structures that exhibit poor performance. Due to the high costs associated with…
This paper is concerned with an inverse obstacle problem for the Laplace's equation. The aim is to recover the constant conductivity coefficient in the equation and the boundary of a Dirichlet polygonal obstacle from a single pair of Cauchy…
We study the inverse problem of reconstructing an incompressible velocity field $\boldsymbol{v}$ from observations of the induced magnetic field $\boldsymbol{b}$. In the presence of a strong, constant background field $\mathbf{F}$, the…
The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…
This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…
In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results,…
The long-time existence and umbilicity estimates for compact, graphical solutions to expanding curvature flows are deduced in Riemannian warped products of a real interval with a compact fibre. Notably we do not assume the ambient manifold…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
We analyze the inverse problem of recovering geometric information from the return map induced by a round-trip between a convex core C and an admissible domain. This process defines a discrete dynamical system on the boundary of C governed…
For semilinear wave equations on Lorentzian manifolds with quadratic derivative non-linear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from…
In these two lectures we shall discuss how the cavity approach can be used efficiently to study optimization problems with global (topological) constraints and how the same techniques can be generalized to study inverse problems in…
We construct counterexamples to inverse problems for the wave operator on domains in $\mathbb{R}^{n+1}$, $n \ge 2$, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which…
In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
Einstein equations are addressed with the energy-momentum tensor that appears if the equations under discussion are required to possess conformal invariance. It is proved that thus derived equations (equations of conformally invariant…
We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with…
We study singularities of surfaces which are given by Kenmotsu-type formula with prescribed unbounded mean curvature.
We consider the inverse problem in geophysics of imaging the subsurface of the Earth in cases where a region below the surface is known to be formed by strata of different materials and the depths and thicknesses of the strata and the…
We consider the inverse source problem of a fixed wavenumber: study properties of an acoustic source based on a single far- or near-field measurement. We show that nonradiating sources having a convex or non-convex corner or edge on their…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…