Related papers: Restoring the Discontinuous Heat Equation Source U…
In this work we investigate the inverse problem of recovering one point source in the heat equation from sparse boundary measurement, i.e., the flux data at several points on the boundary. We prove the unique recovery of the location and…
This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness 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 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…
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…
In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary…
We present a novel method for reconstructing the thermal conductivity coefficient in 1D and 2D heat equations using moving sensors that dynamically traverse the domain to record sparse and noisy temperature measurements. We significantly…
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…
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…
This paper delves into the Inverse Stefan problem, specifically focusing on determining the time-dependent source coefficient in the parabolic heat equation governing heat transfer in a semi-infinite rod. The problem entails the intricate…
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…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem…
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…
Inverse source localization from Helmholtz boundary data collected over a narrow aperture is highly ill-posed and severely undersampled, undermining classical solvers (e.g., the Direct Sampling Method). We present a modular framework that…
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.…
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 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…
In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a…
This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data,…