Related papers: Inverse source problem for the parabolic equation …
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)…
This paper is concerned with identification of a spatial source function from final time observation in a bi-parabolic equation, where the full source function is assumed to be a product of time dependent and a space dependent function. Due…
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…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic…
Stochastic parabolic equations are widely used to model many random phenomena in natural sciences, such as the temperature distribution in a noisy medium, the dynamics of a chemical reaction in a noisy environment, or the evolution of the…
Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
In this paper, we study two types of inverse problems for space semi-discrete stochastic parabolic equations in arbitrary dimensions. The first problem concerns a semi-discrete inverse source problem, which involves determining the random…
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…
In this paper, we consider an inverse problem to determine a semilinear term of a parabolic equation from a single boundary measurement of Neumann type. For this problem, a reconstruction algorithm is established by the spectral…
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…
This paper is devoted to the study of source reconstruction algorithms for coupled systems of heat equations, with either constant or spatially dependent coupling terms, where internal measurements are available from a reduced number of…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multi-frequency phaseless data. In the first stage, we introduce some…
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…
We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…
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 paper deals with the numerical methods for the reconstruction of source term in linear parabolic equation from final overdetermination. We assume that the source term has the form f(x)h(t) and h(t) is given, which guarantees the…
In this paper we investigate direct and inverse problems for time-fractional pseudo-parabolic equations associated with the Jacobi operator. The existence and uniqueness of the solutions are proved. Also, the stability result of the inverse…