Background and activities

I am Professor at the Department of Mathematical Sciences. I have a MSc and a PhD in Mathematics from the University of Vienna, Austria.

My research focuses on non-linear partial differential equations that govern the motion of waves. These equations also model wave phenomena such as wave breaking. I investigate, with the help of mathematical methods, which influence a wave phenomenon has on the future shape of a wave for a given wave profile.

Current projects

I am currently supervising 6 PhD students.

Preprints

  • K. Grunert and A. Reigstad, Traveling waves for the nonlinear variational wave equation, arXiv:2009.03178.
  • K. Grunert and A. Reigstad, A regularized system for the nonlinear variational wave equation, arXiv:2008.13003.
  • S. T. Galtung and K. Grunert, A numerical study of variational discretizations of the Camassa--Holm equation, arXiv:2006.15562.
  • K. Grunert, A. Nordli, and S. Solem, Numerical conservative solutions of the Hunter-Saxton equation, arXiv:2005.03882.

Scientific, academic and artistic work

A selection of recent journal publications, artistic productions, books, including book and report excerpts. See all publications in the database

Journal publications

Part of book/report

  • Grunert, Katrin; Holden, Helge; Grasmair, Markus. (2018) On the Equivalence of Eulerian and Lagrangian Variables for the Two-Component Camassa–Holm System. Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg.
  • Raynaud, Xavier; Grunert, Katrin. (2018) Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system. Non-linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis: The Helge Holden Anniversary Volume.
  • Grunert, Katrin; Holden, Helge; Raynaud, Xavier. (2014) Lipschitz metric for the two-component Camassa-Holm system. Hyperbolic Problems: Theory, Numerics, Applications.
  • Grunert, Katrin; Holden, Helge; Raynaud, Xavier. (2013) Periodic conservative solutions for the two-component Camassa-Holm system. Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday.