Related papers: Identification of matrix diffusion coefficients in…
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…
In this paper we study the inverse problem of identifying the diffusion matrix in an elliptic PDE from measurements. The convex energy functional method with Tikhonov regularization is applied to tackle this problem. For the discretization…
In this work, we present a novel error analysis for recovering a spatially dependent diffusion coefficient in an elliptic or parabolic problem. It is based on the standard regularized output least-squares formulation with an $H^1(\Omega)$…
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…
In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition as well as the state in the Neumann boundary value problem for an elliptic partial differential…
In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…
Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…
This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle…
We exploit the similarities between Tikhonov regularization and Bayesian hierarchical models to propose a regularization scheme that acts like a distributed Tikhonov regularization where the amount of regularization varies from component to…
In this paper, we consider an inverse problem to determine a source term in a parabolic equation, where the data are obtained at a certain time. In general, this problem is ill-posed, therefore the Tikhonov regularization method is proposed…
In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear…
We consider the inverse problem of identification of degenerate diffusion coefficient of the form $x^\alpha a(x)$ in a one dimensional parabolic equation by some extra data. We first prove by energy methods the uniqueness and Lipschitz…
The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the…
This paper studies the inverse problem of determination the history for a stochastic diffusion process, by means of the value at the final time $T$. By establishing a new Carleman estimate, the conditional stability of the problem is…
Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…
Accurate determination of the regularization parameter in inverse problems still represents an analytical challenge, owing mainly to the considerable difficulty to separate the unknown noise from the signal. We present a new approach for…
Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional…
This paper deals with the problem of identification of a Robin coefficient (also known as impedance coefficient) in a parabolic PDE from terminal observations of the temperature distributions. The problem is ill-posed in the sense that…
An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…
In this paper we utilise new methods of Calculus of Variations in $L^\infty$ to provide a regularisation strategy to the ill-posed inverse problem of identifying the source of a non-homogeneous linear elliptic equation, satisfying Dirichlet…