Dr. Katharina Hopf

Weierstrass Institute for Applied Analysis and Stochastics
Research Group Partial Differential Equations

Research interests

  • Analysis of nonlinear partial differential equations
  • Multi-component systems, mixtures and complex flows in physics and biology
  • Entropy methods, stability estimates, asymptotic analysis
  • Well-posedness, qualitative properties, singularities in evolution equations


- Hyperbolic-parabolic normal form and local classical solutions for cross-diffusion systems with incomplete diffusion.
Pierre-Etienne Druet, Katharina Hopf, and Ansgar Jüngel.
Preprint. (Under Revision in CPDE)
- Singularities in L1-supercritical Fokker-Planck equations: A qualitative analysis.
Katharina Hopf.
Preprint. (Accepted for publication in Ann. Inst. H. Poincaré C Anal. Non Linéaire)
- Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models.
Thomas Eiter, Katharina Hopf, and Robert Lasarzik.
Adv. Nonlinear Anal. (2023).
- On multi-species diffusion with size exclusion.
Katharina Hopf and Martin Burger.
Nonlinear Anal. (2022).
- Weak-strong uniqueness for energy-reaction-diffusion systems.
Katharina Hopf.
Math. Models Methods Appl. Sci. (2022).
- Leray-Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress-strain relation.
Thomas Eiter, Katharina Hopf, and Alexander Mielke.
Nonlinear Anal. Real World Appl. (2022).
- Global existence analysis of energy-reaction-diffusion systems.
Julian Fischer, Katharina Hopf, Michael Kniely, and Alexander Mielke.
SIAM J. Math. Anal. (2022).
- Numerical study of Bose-Einstein condensation in the Kaniadakis-Quarati model for bosons.
José A. Carrillo, Katharina Hopf, and Marie-Therese Wolfram.
Kinet. Relat. Models (2020).
- On the singularity formation and relaxation to equilibrium in 1D Fokker-Planck model with superlinear drift.
José A. Carrillo, Katharina Hopf, and José L. Rodrigo.
Adv. Math. (2020).
- Aggregation equations with fractional diffusion: preventing concentration by mixing.
Katharina Hopf and José L. Rodrigo.
Commun. Math. Sci. (2018).