Research interests

My research is centred around analytical and structural aspects of nonlinear evolution partial differential equations arising in the natural sciences. I work on the analysis of multi-component diffusion systems and cross-diffusive couplings with variational origins, and more generally on problems motivated by mixture and multiphase modelling. My current research focuses on degenerate diffusion systems and systems of mixed type in several space dimensions, as well as on boundary and interface effects in reaction-diffusion processes.

• Analysis of nonlinear partial differential equations
• Cross-diffusion, reaction-diffusion; interface phenomena
• Low regularity solutions and singularities
• Entropy tools, variational methods, and gradient flows
• Mixed-type systems of PDEs

Publications in mathematics

-	Renormalised solutions to reaction-diffusion systems with interface conditions: Global existence and weak-strong uniqueness. Katharina Hopf and Bao Quoc Tang. Preprint.
-	Well-posedness and relaxation in a simplified model for viscoelastic phase separation via Hilbertian gradient flows. Moritz Immanuel Gau and Katharina Hopf. Preprint.
-	Interface dynamics in a degenerate Cahn-Hilliard model for viscoelastic phase separation. Katharina Hopf, John King, Andreas Münch, and Barbara Wagner. Interfaces and Free Boundaries (Online first).
-	On the equilibrium solutions of electro-energy-reaction-diffusion systems. Katharina Hopf, Michael Kniely, and Alexander Mielke. ESAIM: Control, Optimisation and Calculus of Variations (2026).
-	Convergence of a finite volume scheme and dissipative measure-valued-strong stability for a hyperbolic-parabolic cross-diffusion system. Katharina Hopf and Ansgar Jüngel. Numerische Mathematik (2025).
-	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).

PhD Thesis

-	On the singularity formation and long-time asymptotics in a class of nonlinear Fokker-Planck equations. Katharina Hopf (Warwick 2019). For this dissertation, I was awarded the 2020 Faculty Thesis Prize for Mathematics (University of Warwick).

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. Chemical Engineering Journal (2025).