4 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…
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…