Research interests

• Analysis of nonlinear partial differential equations
• Quasi-linear degenerate parabolic and hyperbolic-parabolic systems
• Cross-diffusion, mixtures and multi-phase flow
• Entropy tools and variational methods
• Singularities in evolution equations

Publications in mathematics

-	Interface dynamics in a degenerate Cahn-Hilliard model for viscoelastic phase separation. Katharina Hopf, John King, Andreas Münch, and Barbara Wagner. Preprint.
-	On the equilibrium solutions of electro-energy-reaction-diffusion systems. Katharina Hopf, Michael Kniely, and Alexander Mielke. Preprint.
-	Convergence of a finite volume scheme and dissipative measure-valued-strong stability for a hyperbolic-parabolic cross-diffusion system. Katharina Hopf and Ansgar Jüngel. Preprint (under review since 04/23).
-	Singularities in L1-supercritical Fokker-Planck equations: A qualitative analysis. Katharina Hopf. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024).
-	Hyperbolic-parabolic normal form and local classical solutions for cross-diffusion systems with incomplete diffusion. Pierre-Etienne Druet, Katharina Hopf, and Ansgar Jüngel. Comm. Partial Differential Equations (2023).
-	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).

Output from interdisciplinary collaborations

-	Transport of heat and mass for reactive gas mixtures in porous media: modeling and application. David Brust, Katharina Hopf, Jürgen Fuhrmann, Andrii Cheilytko, Michael Wullenkord, Christian Sattler. Preprint.