55 citations · 598 across the 84 of their papers we have counts for
9 papers · 1 filter
On Fokker-Planck Equations with In- and Outflow of Mass
Martin Burger, Ina Humpert, Jan-Frederik Pietschmann
Motivated by modeling transport processes in the growth of neurons, we present results on (nonlinear) Fokker-Planck equations where the total mass is not conserved. This is either…
Strong solutions and weak-strong stability in a system of cross-diffusion equations
Judith Berendsen, Martin Burger, Virginie Ehrlacher +1
Proving the uniqueness of solutions to multi-species cross-diffusion systems is a difficult task in the general case, and there exist very few results in this direction. In this wo…
Mean field models for segregation dynamics
Martin Burger, Jan-Frederik Pietschmann, Helene Ranetbauer +2
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the…
Solution Paths of Variational Regularization Methods for Inverse Problems
Leon Bungert, Martin Burger
We consider a family of variational regularization functionals for a generic inverse problem, where the data fidelity and regularization term are given by powers of a Hilbert norm…
A mesoscopic model of biological transportation networks
Martin Burger, Jan Haskovec, Peter Markowich +1
We introduce a mesoscopic model for natural network formation processes, acting as a bridge between the discrete and continuous network approach proposed by Hu and Cai. The models…
Convergence rates and structure of solutions of inverse problems with imperfect forward models
Martin Burger, Yury Korolev, Julian Rasch
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem y…
The Inverse Problem of Magnetorelaxometry Imaging
Lea Föcke, Daniel Baumgarten, Martin Burger
The aim of this paper is to provide a solid mathematical discussion of the inverse problem in Magnetorelaxometry Imaging (MRXI), a currently developed technique for quantitative bi…
Unified Models for Second-Order TV-Type Regularisation in Imaging - A New Perspective Based on Vector Operators
Eva-Maria Brinkmann, Martin Burger, Joana Sarah Grah
We introduce a novel regulariser based on the natural vector field operations gradient, divergence, curl and shear. For suitable choices of the weighting parameters contained in ou…
Modern Regularization Methods for Inverse Problems
Martin Benning, Martin Burger
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feas…