Katrin Grunert

About

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, 2016-2022.

I am currently supervising 2 PhD students and mentoring 1 PostDoc.

Preprints

K. Grunert and A. Reigstad, A regularized system for the nonlinear variational wave equation, arXiv:2008.13003.

Publications

2022

Bressan, Alberto; Galtung, Sondre Tesdal; Grunert, Katrin; Nguyen, Khai Tien. (2022) Shock interactions for the Burgers-Hilbert equation. Communications in Partial Differential Equations. volum 47 (9).
Galtung, Sondre Tesdal; Grunert, Katrin. (2022) Stumpons are non-conservative traveling waves of the Camassa–Holm equation. Physica D : Non-linear phenomena. volum 433.
Grunert, Katrin; Holden, Helge. (2022) Uniqueness of conservative solutions for the Hunter–Saxton equation. Research in the Mathematical Sciences. volum 9.
Grunert, Katrin; Tandy, Matthew. (2022) Lipschitz stability for the Hunter-Saxton equation. Journal of Hyperbolic Differential Equations. volum 19 (2).

2021

Galtung, Sondre Tesdal; Grunert, Katrin. (2021) A numerical study of variational discretizations of the Camassa–Holm equation. BIT Numerical Mathematics. volum 61 (4).
Grunert, Katrin; Holden, Helge; Jakobsen, Espen Robstad; Stenseth, Nils Christian. (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. volum 118 (4).
Grunert, Katrin; Holden, Helge; Jakobsen, Espen Robstad; Stenseth, Nils Christian. (2021) Reply to Best and Ashby: The concept of evolutionarily stable strategies (ESS) helps link ecology and evolution. Proceedings of the National Academy of Sciences of the United States of America. volum 118 (18).
Grunert, Katrin; Nordli, Anders Samuelsen; Solem, Susanne. (2021) Numerical conservative solutions of the Hunter–-Saxton equation. BIT Numerical Mathematics. volum 61.
Grunert, Katrin; Reigstad, Audun. (2021) Traveling waves for the nonlinear variational wave equation. SN Partial Differential Equations and Applications (SN PDE). volum 2.

2020

Antonio Carrillo, José; Grunert, Katrin; Holden, Helge. (2020) A Lipschitz metric for the Camassa-Holm equation. Forum of Mathematics, Sigma. volum 8 (e27).

2019

Antonio Carrillo, Jose; Grunert, Katrin; Holden, Helge. (2019) A Lipschitz metric for the Hunter–Saxton equation. Communications in Partial Differential Equations. volum 44 (4).

2018

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.
Grunert, Katrin; Nordli, Anders Samuelsen. (2018) Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter–Saxton system. Journal of Hyperbolic Differential Equations. volum 15 (3).
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.

2014

Grunert, Katrin; Holden, Helge; Raynaud, Xavier. (2014) Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics. Nonlinear Analysis: Real world applications. volum 17 (1).
Grunert, Katrin; Holden, Helge; Raynaud, Xavier. (2014) Lipschitz metric for the two-component Camassa-Holm system. Hyperbolic Problems: Theory, Numerics, Applications.

2013

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.
Grunert, Katrin. (2013) Scattering theory for Schrodinger operators on steplike, almost periodic infinite-gap backgrounds. Journal of Differential Equations. volum 254 (6).
Grunert, Katrin; Holden, Helge; Raynaud, Xavier. (2013) LIPSCHITZ METRIC FOR THE CAMASSA-HOLM EQUATION ON THE LINE. Discrete and Continuous Dynamical Systems. Series A. volum 33 (7).

2012

Grunert, Katrin; Holden, Helge; Raynaud, Xavier Marcel. (2012) GLOBAL CONSERVATIVE SOLUTIONS TO THE CAMASSA-HOLM EQUATION FOR INITIAL DATA WITH NONVANISHING ASYMPTOTICS. Discrete and Continuous Dynamical Systems. Series A. volum 32 (12).
Grunert, Katrin; Holden, Helge; Raynaud, Xavier Marcel. (2012) Global Solutions for the Two-Component Camassa-Holm System. Communications in Partial Differential Equations. volum 37 (12).

2011

Grunert, Katrin; Holden, Helge; Raynaud, Xavier Marcel. (2011) Lipschitz metric for the periodic Camassa-Holm equation. Journal of Differential Equations. volum 250 (3).

Journal publications

Bressan, Alberto; Galtung, Sondre Tesdal; Grunert, Katrin; Nguyen, Khai Tien. (2022) Shock interactions for the Burgers-Hilbert equation. Communications in Partial Differential Equations. volum 47 (9).
Galtung, Sondre Tesdal; Grunert, Katrin. (2022) Stumpons are non-conservative traveling waves of the Camassa–Holm equation. Physica D : Non-linear phenomena. volum 433.
Grunert, Katrin; Holden, Helge. (2022) Uniqueness of conservative solutions for the Hunter–Saxton equation. Research in the Mathematical Sciences. volum 9.
Grunert, Katrin; Tandy, Matthew. (2022) Lipschitz stability for the Hunter-Saxton equation. Journal of Hyperbolic Differential Equations. volum 19 (2).
Galtung, Sondre Tesdal; Grunert, Katrin. (2021) A numerical study of variational discretizations of the Camassa–Holm equation. BIT Numerical Mathematics. volum 61 (4).
Grunert, Katrin; Holden, Helge; Jakobsen, Espen Robstad; Stenseth, Nils Christian. (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. volum 118 (4).
Grunert, Katrin; Holden, Helge; Jakobsen, Espen Robstad; Stenseth, Nils Christian. (2021) Reply to Best and Ashby: The concept of evolutionarily stable strategies (ESS) helps link ecology and evolution. Proceedings of the National Academy of Sciences of the United States of America. volum 118 (18).
Grunert, Katrin; Nordli, Anders Samuelsen; Solem, Susanne. (2021) Numerical conservative solutions of the Hunter–-Saxton equation. BIT Numerical Mathematics. volum 61.
Grunert, Katrin; Reigstad, Audun. (2021) Traveling waves for the nonlinear variational wave equation. SN Partial Differential Equations and Applications (SN PDE). volum 2.
Antonio Carrillo, José; Grunert, Katrin; Holden, Helge. (2020) A Lipschitz metric for the Camassa-Holm equation. Forum of Mathematics, Sigma. volum 8 (e27).
Antonio Carrillo, Jose; Grunert, Katrin; Holden, Helge. (2019) A Lipschitz metric for the Hunter–Saxton equation. Communications in Partial Differential Equations. volum 44 (4).
Grunert, Katrin; Nordli, Anders Samuelsen. (2018) Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter–Saxton system. Journal of Hyperbolic Differential Equations. volum 15 (3).
Eckhardt, Jonathan; Grunert, Katrin. (2017) A Lagrangian view on complete integrability of the conservative Camassa– Holm flow. Journal of Integrable systems.
Grunert, Katrin. (2016) Solutions of the Camassa-Holm equation with accumulating breaking times. Dynamics of Partial Differential Equations. volum 13 (2).
Grunert, Katrin; Holden, Helge. (2016) The general peakon-antipeakon solution for the Camassa-Holm equation. Journal of Hyperbolic Differential Equations. volum 13 (2).
Grunert, Katrin; Nguyen, Khai Tien. (2016) On the Burgers–Poisson equation. Journal of Differential Equations. volum 261 (6).
Grunert, Katrin. (2015) Blow-up for the two-component Camassa-Holm system. Discrete and Continuous Dynamical Systems. Series A. volum 35 (5).
Grunert, Katrin; Holden, Helge; Raynaud, Xavier. (2015) A continuous interpolation between conservative and dissipative solutions. Forum of Mathematics, Sigma.
Grunert, Katrin; Holden, Helge; Raynaud, Xavier. (2015) A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system. Forum of Mathematics, Sigma. volum 3.
Grunert, Katrin; Holden, Helge; Raynaud, Xavier. (2014) Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics. Nonlinear Analysis: Real world applications. volum 17 (1).
Grunert, Katrin. (2013) Scattering theory for Schrodinger operators on steplike, almost periodic infinite-gap backgrounds. Journal of Differential Equations. volum 254 (6).
Grunert, Katrin; Holden, Helge; Raynaud, Xavier. (2013) LIPSCHITZ METRIC FOR THE CAMASSA-HOLM EQUATION ON THE LINE. Discrete and Continuous Dynamical Systems. Series A. volum 33 (7).
Grunert, Katrin; Holden, Helge; Raynaud, Xavier Marcel. (2012) GLOBAL CONSERVATIVE SOLUTIONS TO THE CAMASSA-HOLM EQUATION FOR INITIAL DATA WITH NONVANISHING ASYMPTOTICS. Discrete and Continuous Dynamical Systems. Series A. volum 32 (12).
Grunert, Katrin; Holden, Helge; Raynaud, Xavier Marcel. (2012) Global Solutions for the Two-Component Camassa-Holm System. Communications in Partial Differential Equations. volum 37 (12).
Grunert, Katrin; Holden, Helge; Raynaud, Xavier Marcel. (2011) Lipschitz metric for the periodic Camassa-Holm equation. Journal of Differential Equations. volum 250 (3).

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.

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