Related papers: A new regularization method for a parameter identi…
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 provide a convergence analysis of some variational methods alternative to the classical Tikhonov regularization, namely Ivanov regularization (also called method of quasi solutions) with some versions of the discrepancy…
This paper investigates the convergence rate for Tikhonov regularization of the problem of identifying the coefficient $a \in L^{\infty}(\Omega)$ in the Robin-boundary equation $-\mathrm{div}(a\nabla u)-bu=f,~ x \in \Omega \subset \mathbb…
We consider the reconstruction of a diffusion coefficient in a quasilinear elliptic problem from a single measurement of overspecified Neumann and Dirichlet data. The uniqueness for this parameter identification problem has been established…
In this paper, we mainly establish the existence of at least three non-trivial solutions for a class of nonhomogeneous quasilinear elliptic systems with Dirichlet boundary value or Neumann boundary value in a bounded domain…
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…
This paper presents new results allowing an unknown non-Gaussian positive matrix-valued random field to be identified through a stochastic elliptic boundary value problem, solving a statistical inverse problem. A new general class of…
In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…
We consider the identification of scattering and absorption rates in the stationary radiative transfer equation. For a stable solution of this parameter identification problem, we consider Tikhonov regularization within Banach spaces. A…
Evolutionary deep neural networks have emerged as a rapidly growing field of research. This paper studies numerical integrators for such and other classes of nonlinear parametrizations $ u(t) = \Phi(\theta(t)) $, where the evolving…
A key observation underlying this paper is the fact that the range invariance condition for convergence of regularization methods for nonlinear ill-posed operator equations -- such as coefficient identification in partial differential…
Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated…
We give a survey of nonlinear potential estimates and their applications obtained recently for positive solutions to sublinear problems of the type \[ u = \mathbf{G}(\sigma u^q) + f \quad \textrm{in} \,\, \Omega, \] where $0 < q < 1$,…
This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is…
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…
The aim of this paper is to numerically study the performance of a method of regularization. This technique was developed to solve the illposed problem of estimating a source-dimensional Poisson equation for two dimensions from measurements…
Parameter identification problems for partial differential equations are an important subclass of inverse problems. The parameter-to-state map, which maps the parameter of interest to the respective solution of the PDE or state of the…
In this contribution we show sufficient conditions for simultaneous unique identification of unknown spacewise coefficients and heat source in a parabolic partial differential equation given additional final time measurements. Our approach…
Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…
We study a source identification problem for a prototypical elliptic PDE from Dirichlet boundary data. This problem is ill-posed, and the involved forward operator has a significant nullspace. Standard Tikhonov regularization yields…