55 citations · 598 across the 84 of their papers we have counts for
36 papers · 1 filter
Sharp interface analysis of a diffuse interface model for cell blebbing with linker dynamics
Philipp Nöldner, Martin Burger, Harald Garcke
We investigate the convergence of solutions of a recently proposed diffuse interface/phase field model for cell blebbing by means of matched asymptotic expansions. It is a biologic…
Covariance-modulated optimal transport and gradient flows
Martin Burger, Matthias Erbar, Franca Hoffmann +2
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics…
Analysis of Kinetic Models for Label Switching and Stochastic Gradient Descent
Martin Burger, Alex Rossi
In this paper we provide a novel approach to the analysis of kinetic models for label switching, which are used for particle systems that can randomly switch between gradient flows…
Porous medium equation and cross-diffusion systems as limit of nonlocal interaction
Martin Burger, Antonio Esposito
This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a…
On multi-species diffusion with size exclusion
Katharina Hopf, Martin Burger
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpo…
Kinetic Equations for Processes on Co-evolving Networks
Martin Burger
The aim of this paper is to derive macroscopic equations for processes on large co-evolving networks, examples being opinion polarization with the emergence of filter bubbles or ot…
Dynamic optimal transport on networks
Martin Burger, Ina Humpert, Jan-Frederik Pietschmann
We study a dynamic optimal transport problem on a network. Despite the cost for transport along the edges, an additional cost, scaled with a parameter , has to be paid for inter…
On inverse problems for semiconductor equations
M. Burger, H. W. Engl, A. Leitão +1
This paper is devoted to the investigation of inverse problems related to stationary drift-diffusion equations modeling semiconductor devices. In this context we analyze several id…
Network structured kinetic models of social interactions
Martin Burger
The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics t…
Delayed Blow-Up for Chemotaxis Models with Local Sensing
Martin Burger, Philippe Laurençot, Ariane Trescases
The aim of this paper is to analyze a model for chemotaxis based on a local sensing mechanism instead of the gradient sensing mechanism used in the celebrated minimal Keller-Segel…
Coarse graining of a Fokker-Planck equation with excluded volume effects preserving the gradient-flow structure
Maria Bruna, Martin Burger, José Antonio Carrillo
The propagation of gradient flow structures from microscopic to macroscopic models is a topic of high current interest. In this paper we discuss this propagation in a model for the…
Structural analysis of an -infinity variational problem and relations to distance functions
Leon Bungert, Yury Korolev, Martin Burger
In this work we analyse the functional defined on Lipschitz functions with homogeneous Dirichlet boundary conditions. Our analysis is performed di…
Segregation and Gap Formation in Cross-Diffusion Models
M. Burger, J. A. Carrillo, J. -F. Pietschmann +1
In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect t…
Asymptotic Profiles of Nonlinear Homogeneous Evolution Equations of Gradient Flow Type
Leon Bungert, Martin Burger
This work is concerned with the gradient flow of absolutely -homogeneous convex functionals on a Hilbert space, which we show to exhibit finite () or infinite extinction ti…
A PDE model for bleb formation and interaction with linker proteins
Philipp Werner, Martin Burger, Jan-Frederik Pietschmann
The aim of this paper is to further develop mathematical models for bleb formation in cells, including cell-membrane interactions with linker proteins. This leads to nonlinear reac…
On a Class of Singularly Perturbed Elliptic Systems with Asymptotic Phase Segregation
Farid Bozorgnia, Martin Burger
This work is devoted to study of a class of elliptic singular perturbed systems and their singular limit to a phase segregating system. We prove existence and uniqueness and study…
Nonlinear Spectral Decompositions by Gradient Flows of One-Homogeneous Functionals
Leon Bungert, Martin Burger, Antonin Chambolle +1
This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in an infinite-dimens…
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…
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…
On a Reaction-Cross-Diffusion System Modelling the Growth of Glioblastoma
Martin Burger, Patricia Friele, Jan-Frederik Pietschmann
We investigate a recently proposed cross-diffusion system modelling the growth of gliobastoma taking into account size exclusion both in the migration and proliferation process. In…
Asymptotic gradient flow structures of a nonlinear Fokker-Planck equation
Maria Bruna, Martin Burger, Helene Ranetbauer +1
In this paper we consider a nonlinear Fokker-Planck equation with asymptotically small parameters. It describes the diffusion of finite-size particles in the presence of a fixed di…
Sorting Phenomena in a Mathematical Model For Two Mutually Attracting/Repelling Species
Martin Burger, Marco Di Francesco, Simone Fagioli +1
Macroscopic models for systems involving diffusion, short-range repulsion, and long-range attraction have been studied extensively in the last decades. In this paper we extend the…