Katrin Grunert
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
- Member of NTNU's Outstanding Academic Fellows Programme 3.0
- Principal investigator of the RCN Young Research Talent project Wave Phenomena and Stability - a Shocking Combination, 2019-2023.
- Participant in the RCN Toppforsk project Waves and Nonlinear Phenomena, 2016-2021.
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
- (2020) A Lipschitz metric for the Camassa-Holm equation. Forum of Mathematics, Sigma. vol. 8 (e27).
- (2019) A Lipschitz metric for the Hunter–Saxton equation. Communications in Partial Differential Equations. vol. 44 (4).
- (2018) Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter–Saxton system. Journal of Hyperbolic Differential Equations. vol. 15 (3).
- (2017) A Lagrangian view on complete integrability of the conservative Camassa– Holm flow. Journal of Integrable systems.
- (2016) Solutions of the Camassa-Holm equation with accumulating breaking times. Dynamics of Partial Differential Equations. vol. 13 (2).
- (2016) The general peakon-antipeakon solution for the Camassa-Holm equation. Journal of Hyperbolic Differential Equations. vol. 13 (2).
- (2016) On the Burgers–Poisson equation. Journal of Differential Equations. vol. 261 (6).
- (2015) Blow-up for the two-component Camassa-Holm system. Discrete and Continuous Dynamical Systems. Series A. vol. 35 (5).
- (2015) A continuous interpolation between conservative and dissipative solutions. Forum of Mathematics, Sigma.
- (2015) A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system. Forum of Mathematics, Sigma. vol. 3.
- (2014) Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics. Nonlinear Analysis: Real world applications. vol. 17 (1).
- (2013) Scattering theory for Schrodinger operators on steplike, almost periodic infinite-gap backgrounds. Journal of Differential Equations. vol. 254 (6).
- (2013) LIPSCHITZ METRIC FOR THE CAMASSA-HOLM EQUATION ON THE LINE. Discrete and Continuous Dynamical Systems. Series A. vol. 33 (7).
- (2012) GLOBAL CONSERVATIVE SOLUTIONS TO THE CAMASSA-HOLM EQUATION FOR INITIAL DATA WITH NONVANISHING ASYMPTOTICS. Discrete and Continuous Dynamical Systems. Series A. vol. 32 (12).
- (2012) Global Solutions for the Two-Component Camassa-Holm System. Communications in Partial Differential Equations. vol. 37 (12).
- (2011) Lipschitz metric for the periodic Camassa-Holm equation. Journal of Differential Equations. vol. 250 (3).
Part of book/report
- (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.
- (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.
- (2014) Lipschitz metric for the two-component Camassa-Holm system. Hyperbolic Problems: Theory, Numerics, Applications.
- (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.