Related papers: Inverse source problems in elastodynamics
This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…
In this paper, we consider two linear inverse problems for the time-fractional wave equation, assuming that its right-hand side takes the separable form $f(t)h(x)$, where $t \geq 0$ and $x \in \Omega \subset R^N $. The objective is to…
In this work, we investigate the shape identification and coefficient determination associated with two time-dependent partial differential equations in two dimensions. We consider the inverse problems of determining a convex polygonal…
In this work, an inverse problem on the determination of multiple coefficients arising from the time-domain diffuse optical tomography with fluorescence (DOT-FDOT) is investigated. We simultaneously recover the distribution of background…
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…
Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years.…
This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…
This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…
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…
In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time…
A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…
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…
A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…
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 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 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…
In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…
We are concerned with increasing stability in the inverse source problems for the time-dependent Maxwell equations in R^3 , where the source term is compactly supported in both time and spatial variables. By using the Fourier transform,…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
The first part of this paper is concerned with the uniqueness to inverse time-harmonic elastic scattering from bounded rigid obstacles in two dimensions. It is proved that a connected polygonal obstacle can be uniquely identified by the…