33 citations · 303 across the 46 of their papers we have counts for
9 papers · 1 filter
All-at-once versus reduced iterative methods for time dependent inverse problems
Barbara Kaltenbacher
In this paper we investigate all-at-once versus reduced regularization of dynamic inverse problems on finite time intervals . In doing so, we concentrate on iterative method…
Regularization of a backwards parabolic equation by fractional operators
Barbara Kaltenbacher, William Rundell
The backwards diffusion equation is one of the classical ill-posed inverse problems, related to a wide range of applications, and has been extensively studied over the last 50 year…
The Ivanov regularized Gauss-Newton method in Banach space with an a posteriori choice of the regularization radius
Barbara Kaltenbacher, Andrej Klassen, Mario Luiz Previatti de Souza
In this paper we consider the iteratively regularized Gauss-Newton method, where regularization is achieved by Ivanov regularization, i.e., by imposing a priori constraints on the…
Parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging
Barbara Kaltenbacher, Tram Thi Ngoc Nguyen, Anne Wald +1
Magnetic particle imaging (MPI) is a tracer-based technique for medical imaging where the tracer consists of ironoxide nanoparticles. The key idea is to measure the particle respon…
The tangential cone condition for some coefficient identification model problems in parabolic PDEs
Barbara Kaltenbacher, Tram Thi Ngoc Nguyen, Otmar Scherzer
The tangential condition was introduced in [Hanke et al., 95] as a sufficient condition for convergence of the Landweber iteration for solving ill-posed problems. In this paper we…
Recovery of multiple coefficients in a reaction-diffusion equation
Barbara Kaltenbacher, William Rundell
This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity and the potential in a parabolic equation from overposed dat…
On the identification of a nonlinear term in a reaction-diffusion equation
Barbara Kaltenbacher, William Rundell
Reaction-diffusion equations are one of the most common partial differential equations used to model physical phenomenon. They arise as the combination of two physical processes: a…
Vanishing relaxation time limit of the Jordan--Moore--Gibson--Thompson wave equation with Neumann and absorbing boundary conditions
Barbara Kaltenbacher, Vanja Nikolić
We study the Jordan--Moore--Gibson--Thompson (JMGT) equation, a third order in time wave equation that models nonlinear sound propagation, in the practically relevant setting of Ne…
On the Jordan-Moore-Gibson-Thompson equation: well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time
Barbara Kaltenbacher, Vanja Nikolić
In this paper, we consider the Jordan-Moore-Gibson-Thompson equation, a third order in time wave equation describing the nonlinear propagation of sound that avoids the infinite sig…