Katharina Hopf

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

I am a postdoctoral researcher in the PDE group at WIAS, working in the team of Alexander Mielke. Prior to Berlin, I completed my PhD studies at the University of Warwick. For my dissertation, I have recently been awarded the 2020 Faculty of Science Thesis Prize in Mathematics.

E-mail: hopf(at)wias-berlin.de

Research interests: Analysis and PDEs; in particular nonlinear evolution equations arising in physics and biology. Entropy based methods for strongly coupled parabolic systems, reaction-diffusion systems. Variational approaches to the continuum mechanics of soft materials. Singularity formation and blow-up in nonlinear parabolic PDEs, viscosity solutions.

Publications and Preprints:

  • (with T. Eiter and A. Mielke)

    Leray-Hopf solutions to a viscoelastic fluid model with nonsmooth stress-strain relation. Preprint. arXiv:2104.05545

  • Weak-strong uniqueness for energy-reaction-diffusion systems. Preprint. arXiv:2102.02491
  • (with J. Fischer, M. Kniely, and A. Mielke)

    Global existence analysis of energy-reaction-diffusion systems. Preprint. arXiv:2012.03792

  • (with J. A. Carrillo and J. L. Rodrigo)

    On the singularity formation and relaxation to equilibrium in 1D Fokker-Planck model with superlinear drift. Adv. Math. (2020). arXiv:1901.11098

  • (with J. A. Carrillo and M.-T. Wolfram)

    Numerical study of Bose-Einstein condensation in the Kaniadakis-Quarati model for bosons. Kinet. Relat. Models (2020). arXiv:1902.06266

  • (with J. L. Rodrigo)

    Aggregation equations with fractional diffusion: preventing concentration by mixing. Commun. Math. Sci. (2018). arXiv:1703.05578