Related papers: Reconstruction and Solvability for Discontinuous H…
We study the recovery of a spatially dependent source in a one-dimensional space-time fractional wave equation using boundary measurement data collected at a single endpoint. The main challenge arises from the fact that the eigenfunctions…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L_2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
Solution of the discretized Lippmann-Schwinger equation in the spatial frequency domain involves the inversion of a linear operator specified by the scattering potential. To regularize this inevitably ill-conditioned problem, we propose a…
We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, being measured in the direction to a specific boundary…
We study a Sturm-Liouville type eigenvalue problem for second-order differential equations on the infinite interval. Here the eigenfunctions are nonzero solutions exponentially decaying at infinity. We prove that at any discrete eigenvalue…
We show in this paper a Lipschitz stability result for a crack inverse problem in half space. The direct problem is a Laplace equation with zero Neumann condition on the top boundary. The forcing term is a discontinuity across the crack.…
We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient from exterior partial measurements of the…
We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary…
In this paper, we consider forward and inverse problems for subdiffusion equations with time-dependent coefficients. The fractional derivative is taken in the sense of Riemann-Liouville. Using the classical Fourier method, the theorem of…
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
In this article, we study a model problem featuring a L\'evy process in a domain with semi-transparent boundary by considering the following perturbed fractional Laplacian operator \[\mathscr{L}_{b,q} := (-\Delta)^t +…
An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…
We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigenvalue problem posed in a polygonal domain. The algorithm is…
In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
In the paper, we study the problem of recovering the Sturm--Liouville operator with frozen argument from its spectrum and additional data. For this inverse problem, we establish a substantial property of the uniform stability, which…
We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed…