相关论文: Mathematical and numerical study of an inverse sou…

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…

In this paper, we study the inverse random source scattering problem for the biharmonic Schrodinger equation in two and three dimensions. The driven source is assumed to be a generalized microlocally isotropic Gaussian random function whose…

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…

We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The medium has an anisotropic scattering property that is neither…

In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…

This paper presents three quantitative sampling methods for reconstructing extended sources of the biharmonic wave equation using scattered field data. The first method employs an indicator function that solely relies on scattered fields $…

This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is…

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The…

We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted…

We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely…

We propose in this paper a new numerical method to solve an inverse source problem for general hyperbolic equations. This is the problem of reconstructing sources from the lateral Cauchy data of the wave field on the boundary of a domain.…

We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…

For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source…

We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium. Of specific interest, the exiting radiation is measured on an arc. The attenuation and scattering…

In this paper, we study the direct and inverse scattering of the Schr\"odinger equation in a three-dimensional planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the…

Starting with far field data of time-harmonic acoustic or electromagnetic waves radiated by a collection of compactly supported sources in two-dimensional free space, we develop criteria and algorithms for the recovery of the far field…

Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…