Related papers: Unique determination of the damping coefficient in…
We study an inverse problem for the wave equation, concerned with estimating the wave speed, aka velocity, from data gathered by an array of sources and receivers that emit probing signals and measure the resulting waves. The typical…
This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source…
The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the…
This paper is concerned with the inverse moving source problems for parabolic equations. Given the temporal function, we prove the uniqueness of the nonlinear inverse problem of determining the orbit function by final data measured in a…
We consider the stabilization problem on a manifold with boundary for a wave equation with measure-valued linear damping. For a wide class of measures, containing Dirac masses on hypersurfaces as well as measures with fractal support, we…
In this paper, we consider the inverse boundary problems of recovering the time-dependent nonlinearity and damping term for a semilinear wave equation on a Riemannian manifold. The Carleman estimate and the construction of Gaussian beams…
The study of the paper mainly focusses on recovering the dissipative parameter in a cascade system coupling a bilaplacian operator to a heat equation from final time measured data via quasi-solution based optimization. The coefficient…
This paper is devoted to the study of the inverse problem of determining the right-hand side of the subdiffusion equation with the Caputo derivative with respect to time. In our case, the inverse problem consists in restoring the…
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…
The inverse question of identifying a function from the nodes (zeroes) of its wavelet transform arises in a number of fields. These include whether the nodes of a heat or hypoelliptic equation solution determine its initial conditions, and…
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…
In this paper, we obtain the sharp uniqueness for an inverse $x$-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique…
In this work, we study the inverse problem of determining a potential coefficient in an abstract wave equation that includes a lower-order term. The equation incorporates a time-fractional derivative in the Caputo sense, as well as a…
It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are…
We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…
This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…
We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a…
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…
A source of deterministic single photons is proposed and demonstrated by the application of a measurement-based feedback protocol to a heralded single photon source consisting of an ensemble of cold rubidium atoms. Our source is stationary…
This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…