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.
- 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, 2016-2022.
I am currently supervising 2 PhD students and mentoring 1 PostDoc.
- A. Bressan, S.T. Galtung, K. Grunert, and K.T. Nguyen, Shock interactions for the Burgers--Hilbert equation, arXiv:2204.02421.
- K. Grunert and M. Tandy, Lipschitz stability for the Hunter-Saxton equation, arXiv:2103.10227.
- K. Grunert and A. Reigstad, A regularized system for the nonlinear variational wave equation, arXiv:2008.13003.
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
- (2022) Shock interactions for the Burgers-Hilbert equation. Communications in Partial Differential Equations.
- (2022) Stumpons are non-conservative traveling waves of the Camassa–Holm equation. Physica D : Non-linear phenomena. vol. 433.
- (2022) Uniqueness of conservative solutions for the Hunter–Saxton equation. Research in the Mathematical Sciences. vol. 9.
- (2021) A numerical study of variational discretizations of the Camassa–Holm equation. BIT Numerical Mathematics. vol. 61 (4).
- (2021) Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig–MacArthur predator–prey model. Proceedings of the National Academy of Sciences of the United States of America. vol. 118 (4).
- (2021) Numerical conservative solutions of the Hunter–-Saxton equation. BIT Numerical Mathematics. vol. 61.
- (2021) Traveling waves for the nonlinear variational wave equation. SN Partial Differential Equations and Applications (SN PDE). vol. 2.
- (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).