Related papers: Identification of a Point Source in the Heat Equat…
In this work the authors consider the recovery of the point source in the heat equation. The used data is the sparse boundary measurements. The uniqueness theorem of the inverse problem is given. After that, the numerical reconstruction is…
This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…
We consider the recovery of a source term $f(x,t)=p(x)q(t)$ for the nonhomogeneous heat equation in $\Omega\times (0,\infty)$ where $\Omega$ is a bounded domain in $\mathbb{R}^2$ with smooth boundary $\partial\Omega$ from overposed lateral…
We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…
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…
In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system…
This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…
We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information…
We study an inverse parabolic problem of identifying two source terms in heat equation with dynamic boundary conditions from a final time overdetermination data. Using a weak solution approach by Hasanov, the associated cost functional is…
We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical Tikhonov regularization, we propose a novel approach based on…
In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…
An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…
The paper considers an inverse source problem for a one-dimensional time-fractional heat equation with the generalized impedance boundary condition. The inverse problem is the time dependent source parameter identification together with the…
We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…
This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…
This paper investigates an inverse random source problem for stochastic evolution equations, including stochastic heat and wave equations, with the unknown source modeled as $g(x)f(t)\dot{W}(t)$. The research commences with the…
In this paper, the focus is on the reconstruction of a diffusive field and the localization of the underlying driving sources on arbitrary graphs by observing a significantly smaller subset of vertices of the graph uniformly in time.…
This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while in an incompletely known medium. We prove that the boundary…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
In this work we investigate the unique identifiability and stable recovery of a spatially dependent variable-order in the subdiffusion model from the boundary flux measurement. We establish several new unique identifiability results from…