Related papers: Restoring the Discontinuous Heat Equation Source U…
We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…
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 work presents a mathematical model to enable rapid prediction of airborne contaminant transport based on scarce sensor measurements. The method is designed for applications in critical infrastructure protection (CIP), such as…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
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…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
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…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…
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…
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…
The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
This paper is concerned with a practical inverse problem of simultaneously reconstructing the surface heat flux and the thickness of a solid structure from the associated ultrasonic measurements. In a thermoacoustic coupling model, the…
Temperature monitoring during the life time of heat source components in engineering systems becomes essential to guarantee the normal work and the working life of these components. However, prior methods, which mainly use the interpolate…
For the heat equation in a bounded domain we give a stability result for a smooth diffusion coefficient. The key ingredients are a global Carleman-type estimate, a Poincar\'e-type estimate and an energy estimate with a single observation…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…
This article is devoted to inverse problems of recovering point sources in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of these inverse problems with pointwise overdetermination…
We study inverse boundary problems for evolutionary PDEs using only a single passive boundary observation, where data from an unknown internal source propagate through an unknown medium without active inputs. The goal is the simultaneous…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…