10 citations · 16 across the 10 of their papers we have counts for
12 papers
Partial Hölder Regularity for Solutions of a Class of Cross-Diffusion Systems with Entropy Structure
Marcel Braukhoff, Claudia Raithel, Nicola Zamponi
In this article we show a -partial regularity result for solutions of a certain class of cross-diffusion systems with entropy structure. Under slightly more stringent cond…
Global martingale solutions for stochastic Shigesada-Kawasaki-Teramoto population models
Marcel Braukhoff, Florian Huber, Ansgar Jüngel
The existence of global nonnegative martingale solutions to cross-diffusion systems of Shigesada-Kawasaki-Teramoto type with multiplicative noise is proven. The model describes the…
Quantitative dynamics of irreversible enzyme reaction-diffusion systems
Marcel Braukhoff, Amit Einav, Bao Quoc Tang
In this work we investigate the convergence to equilibrium for mass action reaction-diffusion systems which model irreversible enzyme reactions. Using the standard entropy method i…
Partial Hölder Regularity for Bounded Solutions of a Class of Cross-Diffusion Systems with Entropy Structure
Marcel Braukhoff, Claudia Raithel, Nicola Zamponi
In this contribution we obtain partial -regularity for bounded solutions of a certain class of cross-diffusion systems, which are strongly coupled, degenerate quasilinear…
An entropy structure preserving space-time formulation for cross-diffusion systems: Analysis and Galerkin discretization
Marcel Braukhoff, Ilaria Perugia, Paul Stocker
Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical c…
Entropy-dissipating finite-difference schemes for nonlinear fourth-order parabolic equations
Marcel Braukhoff, Ansgar Jüngel
Structure-preserving finite-difference schemes for general nonlinear fourth-order parabolic equations on the one-dimensional torus are derived. Examples include the thin-film and t…
Global solutions for chemotaxis-Navier-Stokes system with Robin boundary conditions
Marcel Braukhoff, Bao Quoc Tang
We consider a chemotaxis-Navier-Stokes system modelling cellular swimming in fluid drops where an exchange of oxygen between the drop and its environment is taken into account. Thi…
A structure-preserving discontinuous Galerkin scheme for the Fischer-KPP equation
Francesca Bonizzoni, Marcel Braukhoff, Ansgar Jüngel +1
An implicit Euler discontinuous Galerkin scheme for the Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP) equation for population densities with no-flux boundary conditions is sug…
Stationary solutions to a chemotaxis-consumption model with realistic boundary conditions
Marcel Braukhoff, Johannes Lankeit
Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest…
Global analytic solutions of the semiconductor Boltzmann-Dirac-Benney equation with relaxation time approximation
Marcel Braukhoff
The global existence of a solution of the semiconductor Boltzmann-Dirac-Benney equation \[ \partial_t f + \nablaε(p)\cdot\nabla_x f - \nabla ρ_f(x,t)\cdot\nabla_p f = \frac{\mathca…
Semiconductor Boltzmann-Dirac-Benney equation with BGK-type collision operator: existence of solutions vs. ill-posedness
Marcel Braukhoff
A semiconductor Boltzmann equation with a non-linear BGK-type collision operator is analyzed for a cloud of ultracold atoms in an optical lattice: \[ \partial_t f + \nabla_pε(p)\cd…
Energy-transport systems for optical lattices: derivation, analysis, simulation
Marcel Braukhoff, Ansgar Jüngel
Energy-transport equations for the transport of fermions in optical lattices are formally derived from a Boltzmann transport equation with a periodic lattice potential in the diffu…