18 citations · 51 across the 10 of their papers we have counts for
10 papers
Linearized uniqueness of space dependent coefficients in a non-autonomous evolution equation from non-local observations
Barbara Kaltenbacher
In this paper, we consider identification of space dependent coefficients in a time dependent PDE, which is non-autonomous, due to a bilinear control term. We prove linearized uniq…
Identification of space-dependent coefficients in two competing terms of a nonlinear subdiffusion equation
Barbara Kaltenbacher, William Rundell
We consider a (sub)diffusion equation with a nonlinearity of the form , where and are space dependent functions. Prominent examples are the Fisher-KPP, the Frank-…
Decay rates to equilibrium in a nonlinear subdiffusion equation with two counteracting terms
Barbara Kaltenbacher
In this paper we prove convergence to a steady state as for solutions to the subdiffusion equation \[ \partial_t^αu - \mathbb{L} u = q(x)u - p(x)f(u) + r \] with the e…
Locally-averaged McCormick relaxations for discretization-regularized inverse problems
Barbara Kaltenbacher, Paul Manns
In this paper, by means of a standard model problem, we devise an approach to computing approximate dual bounds for use in global optimization of coefficient identification in part…
Reconstruction of space-dependence and nonlinearity of a reaction term in a subdiffusion equation
Barbara Kaltenbacher, William Rundell
In this paper we study the simultaneous reconstruction of two coefficients in a reaction-subdiffusion equation, namely a nonlinearity and a space dependent factor. The fact that th…
Integration based profile likelihood calculation for PDE constrained parameter estimation problems
Romana Boiger, Jan Hasenauer, Sabrina Hross +1
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are…
The least error method for sparse solution reconstruction
Kristian Bredies, Barbara Kaltenbacher, Elena Resmerita
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so…
An online parameter identification method for time dependent partial differential equations
Romana Boiger, Barbara Kaltenbacher
Online parameter identification is of importance, e.g., for model predictive control. Since the parameters have to be identified simultaneously to the process of the modeled system…
A convergence rates result for an iteratively regularized Gauss-Newton-Halley method in Banach space
Barbara Kaltenbacher
The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification probems for dif…
Goal oriented adaptivity in the IRGNM for parameter identification in PDEs I:\\ reduced formulation
Barbara Kaltenbacher, Alana Kirchner, Slobodan Veljovi\' c
In this paper we study adaptive discretization of the iteratively regularized Gauss-Newton method IRGNM with an a posteriori (discrepancy principle) choice of the regularization pa…