Related papers: An inverse source problem for the stochastic wave …
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
In this paper, we study an inverse problem for identifying the initial value in a space-time fractional diffusion equation from the final time data. We show the identifiability of this inverse problem by proving the existence of its unique…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and positive discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
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…
In this paper, we study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…
This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…
We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the…
This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order $\alpha\in(0,2]$ in time. In the first problem, the sources are supposed to move along known…
We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in…
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…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…
In this article, we prove a uniqueness result for a coefficient inverse problems regarding a wave, a heat or a Schr\"odinger equation set on a tree-shaped network, as well as the corresponding stability result of the inverse problem for the…
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…
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…
Dealing with the inverse source problem for the scalar wave equation, we have shown recently that we can reconstruct the space-time dependent source function from the measurement of the wave, collected at a single point $x$ for a large…
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…
This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…
In this paper, we study direct and inverse images for fractional stochastic tangent sets and we establish the deterministic necessary and sufficient conditions that guarantee that the solution of a given stochastic differential equation…