16 citations · 86 across the 13 of their papers we have counts for
13 papers
Renormalised solutions to reaction-diffusion systems with interface conditions: Global existence and weak-strong uniqueness
Katharina Hopf, Bao Quoc Tang
We introduce an extension of the concept of renormalised solutions for entropy-dissipating reaction-diffusion systems due to J. Fischer (Arch. Ration. Mech. Anal. 218, 2015) to sys…
On the equilibrium solutions of electro-energy-reaction-diffusion systems
Katharina Hopf, Michael Kniely, Alexander Mielke
Electro-energy-reaction-diffusion systems are thermodynamically consistent continuum models for reaction-diffusion processes that account for temperature and electrostatic effects…
Convergence of a finite volume scheme and dissipative measure-valued-strong stability for a hyperbolic-parabolic cross-diffusion system
Katharina Hopf, Ansgar Jüngel
This article is concerned with the development of a theoretical framework of global measure-valued solutions for a class of hyperbolic-parabolic cross-diffusion systems, and its ap…
Hyperbolic-parabolic normal form and local classical solutions for cross-diffusion systems with incomplete diffusion
Pierre-Étienne Druet, Katharina Hopf, Ansgar Jüngel
We investigate degenerate cross-diffusion equations with a rank-deficient diffusion matrix that are considered to model populations which move as to avoid spatial crowding and have…
Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models
Thomas Eiter, Katharina Hopf, Robert Lasarzik
We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and an internal stress. This stress tensor is t…
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…
Singularities in -supercritical Fokker-Planck equations: A qualitative analysis
Katharina Hopf
A class of nonlinear Fokker-Planck equations with superlinear drift is investigated in the -supercritical regime, which exhibits a finite critical mass. The equations have a f…
Leray-Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress-strain relation
Thomas Eiter, Katharina Hopf, Alexander Mielke
We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow…
Weak-strong uniqueness for energy-reaction-diffusion systems
Katharina Hopf
We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems. The systems considered are motivated by ther…
Global existence analysis of energy-reaction-diffusion systems
Julian Fischer, Katharina Hopf, Michael Kniely +1
We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest…
Numerical study of Bose-Einstein condensation in the Kaniadakis-Quarati model for bosons
José A. Carrillo, Katharina Hopf, Marie-Therese Wolfram
Kaniadakis and Quarati (1994) proposed a Fokker--Planck equation with quadratic drift as a PDE model for the dynamics of bosons in the spatially homogeneous setting. It is an open…
On the singularity formation and relaxation to equilibrium in 1D Fokker-Planck model with superlinear drift
José A. Carrillo, Katharina Hopf, José L. Rodrigo
We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function…
Aggregation equations with fractional diffusion: preventing concentration by mixing
Katharina Hopf, José L. Rodrigo
We investigate a class of aggregation-diffusion equations with strongly singular kernels and weak (fractional) dissipation in the presence of an incompressible flow. Without the fl…