Related papers: Reconstruction of source function in a parabolic e…
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 paper, we study an inverse problem of identifying two spatial-temporal source terms in the Schr\"odinger equation with dynamic boundary conditions from the final time overdetermination. We adopt a weak solution approach to solve the…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…
We consider the inverse shape and parameter problem for detecting corrosion from partial boundary measurements. This problem models the non-destructive testing for a partially buried object from electrostatic measurements on the accessible…
This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…
The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR)…
In the present paper, we investigate the initial-boundary value problem for fractional order parabolic equation on a metric star graph in Sobolev spaces. First, we prove the existence and uniqueness results of strong solutions which are…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
This paper is concerned with the inverse moving source problems for parabolic equations. Given the temporal function, we prove the uniqueness of the nonlinear inverse problem of determining the orbit function by final data measured in a…
This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this…
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…
In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…
A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…
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…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the $L^2$-Tikhonov regularization method, we analyze its convergence under two…
In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish novel (weighted) conditional stability estimates under very…
We study an inverse source problem for a semilinear parabolic equation in a bounded domain, where the nonlinearity depends on the unknown function and its gradient through a quadratic reaction term and a Burgers-type convection term. From…
In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…
We study an inverse problem associated with an eddy current model. We first address the ill-posedness of the inverse problem by proving the compactness of the forward map with respect to the conductivity and the non-uniqueness of the…