Related papers: A convergent numerical method for a multi-frequenc…
In this paper, we will study increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain $\Omega$ with sufficiently smooth…
The inverse problem of reconstructing a source term from boundary measurements, for the wave equation, is revisited. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small…
In this paper, we present the analytical and numerical study of the optimization approach for determining the space-dependent source function in the parabolic inverse source problem using partial boundary measurements. The Lagrangian…
This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and…
This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying…
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…
We use the work of Milton, Seppecher, and Bouchitt\'{e} on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In…
This paper is concerned with reconstruction issue of some typical inverse problems and consists of three parts. First a framework of the enclosure method for an inverse source problem governed by the Helmholtz equation at a fixed wave…
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…
In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…
In this work, we consider an inverse problem of determining a time dependent coefficient in a fully fractional diffusion equation with a nonlinear source term. The nonlocal initial-boundary value problem refers to the forward model: the…
We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice $\mathbb{Z}^d$, $d \ge 1$. We consider this problem for the cases with and without phase information. We prove uniqueness results…
We consider a parabolic equation in a bounded domain $\OOO$ over a time interval $(0,T)$ with the homogeneous Neumann boundary condition. We arbitrarily choose a subboundary $\Gamma \subset \ppp\OOO$. Then, we discuss an inverse problem of…
We consider the linear system of viscoelasticity with the homogeneous Dirichlet boundary condition. First we prove a Carleman estimate with boundary values of solutions of viscoelasticity system. Since a solution $u$ under consideration is…
A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the…
We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
To compute the spatially distributed dielectric constant from the backscattering data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve the inverse problem, we establish a new version of Carleman estimate and…
This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…
In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…