Related papers: The uniqueness in the inverse problem for transmis…
This paper is concerned with the inverse diffraction problems by a periodic curve with Dirichlet boundary condition in two dimensions. It is proved that the periodic curve can be uniquely determined by the near-field measurement data…
An uniqueness theorem for the inverse problem in the case of a second-order equation defined on the interval [0,1] when the boundary forms contain combinations of the values of functions at the points 0 and 1 is proved. The auxiliary…
This paper is concerned with uniqueness in inverse electromagnetic scattering with phaseless far-field pattern at a fixed frequency. In our previous work [{\em SIAM J. Appl. Math.} {\bf 78} (2018), 3024-3039], by adding a known reference…
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.…
The spheroidal wave functions are investigated in the case m=1. The integral equation is obtained for them. For the two kinds of eigenvalues in the differential and corresponding integral equations, the relation between them are given…
The quest to reveal the physical essence of the infinitely many symmetries and conservation laws that are intrinsic to integrable systems has historically posed a significant challenge at the confluence of physics and mathematics. This…
The spectrum of a one-dimensional Hamiltonian with potential $V(x)=ix^2$ for negative $x$ and $V(x)=-ix^2$ for positive $x$ is analyzed. The Schr\"odinger equation is algebraically solvable and the eigenvalues are obtained as the zeros of…
We study an inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lam\'e parameters associated to a linear, isotropic fractional elasticity operator from…
We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…
In spherical surface wave tomography, one measures the integrals of a function defined on the sphere along great circle arcs. This forms a generalization of the Funk--Radon transform, which assigns to a function its integrals along full…
In this paper, we investigate the interior transmission eigenvalue problem for an inhomogeneous media with conductive boundary conditions. We prove the discreteness and existence of the transmission eigenvalues. We also investigate the…
We study Sturm--Liouville differential operators on the time scales consisting of a finite number of isolated points and segments. In a previous paper it was established that such operators are uniquely determined by their spectral…
In this paper, we study the problem of uniqueness of a divergence-free velocity field with vorticity given by the Prandtl spiral. We show that if the class of admissible velocities is restricted to those satisfying the velocity matching…
In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…
We consider an initial boundary value problem in a bounded domain $\Omega$ over a time interval $(0, T)$ for a time-fractional wave equation where the order of the fractional time derivative is between $1$ and $2$ and the spatial elliptic…
In this work, we study the inverse spectral problems for the Sturm-Liouville operators on [0,1] with complex coefficients and a discontinuity at $x=a\in(0,1)$. Assume that the potential on (a,1) and some parameters in the discontinuity and…
The reflection and transmission of wave functions at a potential step is a well-known issue in a textbook of quantum mechanics. We studied the reflection and transmission characteristics analytically when the potential step is moving at a…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
Inverse spectral problems for Sturm-Liouville operators on a finite interval with non-separated boundary conditions are studied in the central symmetric case, when the potential is symmetric with respect to the middle of the interval. We…
We consider uniqueness in an inverse Schr\"odinger problem in a bounded domain in $\mathbb{R}^2$ given the Dirichlet-to-Neumann map on part of the boundary. On the remaining boundary we impose a new type of singular boundary condition with…