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.
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, 2019-2024.
- Participant in the RCN Toppforsk project Waves and Nonlinear Phenomena, 2016-2022.
I am currently supervising 1 PhD student.
Research
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.
Publications
Preprints
- S. T. Galtung and K. Grunert, Wave breaking for the nonlinear variational wave equation, arXiv:2502.19889.
- T. Christiansen and K. Grunert, Rate of convergence for numerical α-dissipative solutions of the Hunter-Saxton equation, arXiv:2411.07712.
2025
-
Grunert, Katrin;
Christiansen, Thomas.
(2025)
A numerical view on α -dissipative solutions of the Hunter- Saxton equation.
ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)
Academic article
2024
-
Christiansen, Thomas;
Grunert, Katrin;
Nordli, Anders Samuelsen;
Solem, Susanne.
(2024)
A Convergent Numerical Algorithm for α-Dissipative Solutions of the Hunter–Saxton Equation.
Journal of Scientific Computing
Academic article
-
Grunert, Katrin.
(2024)
Uniqueness of dissipative solutions for the Camassa–Holm equation.
Journal of Differential Equations
Academic article
-
Grunert, Katrin;
Tandy, Matthew Laurence.
(2024)
A Lipschitz metric for α-dissipative solutions to the Hunter–Saxton equation.
SN Partial Differential Equations and Applications (SN PDE)
Academic article
2023
-
Grunert, Katrin;
Reigstad, Audun.
(2023)
A regularized system for the nonlinear variational wave equation.
SN Partial Differential Equations and Applications (SN PDE)
Academic article
2022
-
Bressan, Alberto;
Galtung, Sondre Tesdal;
Grunert, Katrin;
Nguyen, Khai Tien.
(2022)
Shock interactions for the Burgers-Hilbert equation.
Communications in Partial Differential Equations
Academic article
-
Grunert, Katrin;
Tandy, Matthew.
(2022)
Lipschitz stability for the Hunter-Saxton equation.
Journal of Hyperbolic Differential Equations
Academic article
-
Galtung, Sondre Tesdal;
Grunert, Katrin.
(2022)
Stumpons are non-conservative traveling waves of the Camassa–Holm equation.
Physica D : Non-linear phenomena
Academic article
-
Grunert, Katrin;
Holden, Helge.
(2022)
Uniqueness of conservative solutions for the Hunter–Saxton equation.
Research in the Mathematical Sciences
Academic article
2021
-
Galtung, Sondre Tesdal;
Grunert, Katrin.
(2021)
A numerical study of variational discretizations of the Camassa–Holm equation.
BIT Numerical Mathematics
Academic article
-
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 (PNAS)
Letter to the editor
-
Grunert, Katrin;
Reigstad, Audun.
(2021)
Traveling waves for the nonlinear variational wave equation.
SN Partial Differential Equations and Applications (SN PDE)
Academic article
-
Reigstad, Audun;
Grunert, Katrin;
Lindqvist, Peter;
Holden, Helge.
(2021)
A Regularized System for the Nonlinear Variational Wave Equation.
NTNU
Doctoral dissertation
-
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 (PNAS)
Academic article
-
Grunert, Katrin;
Nordli, Anders Samuelsen;
Solem, Susanne.
(2021)
Numerical conservative solutions of the Hunter–-Saxton equation.
BIT Numerical Mathematics
Academic article
2020
-
Antonio Carrillo, José;
Grunert, Katrin;
Holden, Helge.
(2020)
A Lipschitz metric for the Camassa-Holm equation.
Forum of Mathematics, Sigma
Academic article
-
Galtung, Sondre Tesdal;
Holden, Helge;
Grunert, Katrin;
Raynaud, Xavier.
(2020)
Discretizations of Wave Equations and Applications of Variational Principles.
NTNU
Doctoral dissertation
2019
-
Antonio Carrillo, Jose;
Grunert, Katrin;
Holden, Helge.
(2019)
A Lipschitz metric for the Hunter–Saxton equation.
Communications in Partial Differential Equations
Academic article
2018
-
Grunert, Katrin;
Holden, Helge;
Grasmair, Markus.
(2018)
On the Equivalence of Eulerian and Lagrangian Variables for the Two-Component Camassa–Holm System.
Springer Nature
Academic chapter/article/Conference paper
-
Raynaud, Xavier;
Grunert, Katrin.
(2018)
Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system.
European Mathematical Society (EMS) Press
Academic chapter/article/Conference paper
-
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
Academic article
2017
-
Eckhardt, Jonathan;
Grunert, Katrin.
(2017)
A Lagrangian view on complete integrability of the conservative Camassa– Holm flow.
Journal of Integrable systems
Academic article
2016
-
Grunert, Katrin.
(2016)
Solutions of the Camassa-Holm equation with accumulating breaking times.
Dynamics of Partial Differential Equations
Academic article
-
Grunert, Katrin;
Nguyen, Khai Tien.
(2016)
On the Burgers–Poisson equation.
Journal of Differential Equations
Academic article
-
Grunert, Katrin;
Holden, Helge.
(2016)
The general peakon-antipeakon solution for the Camassa-Holm equation.
Journal of Hyperbolic Differential Equations
Academic article
2015
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2015)
A continuous interpolation between conservative and dissipative solutions.
Forum of Mathematics, Sigma
Academic article
-
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
Academic article
-
Grunert, Katrin.
(2015)
Blow-up for the two-component Camassa-Holm system.
Discrete and Continuous Dynamical Systems. Series A
Academic article
2014
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2014)
Lipschitz metric for the two-component Camassa-Holm system.
American Institute of Mathematical Sciences (AIMS) Press
Academic chapter/article/Conference paper
-
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
Academic article
2013
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2013)
Periodic conservative solutions for the two-component Camassa-Holm system.
American Mathematical Society (AMS)
Academic chapter/article/Conference paper
-
Grunert, Katrin.
(2013)
Scattering theory for Schrodinger operators on steplike, almost periodic infinite-gap backgrounds.
Journal of Differential Equations
Academic article
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2013)
LIPSCHITZ METRIC FOR THE CAMASSA-HOLM EQUATION ON THE LINE.
Discrete and Continuous Dynamical Systems. Series A
Academic article
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
Academic article
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier Marcel.
(2012)
Global Solutions for the Two-Component Camassa-Holm System.
Communications in Partial Differential Equations
Academic article
2011
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier Marcel.
(2011)
Lipschitz metric for the periodic Camassa-Holm equation.
Journal of Differential Equations
Academic article
Journal publications
-
Grunert, Katrin;
Christiansen, Thomas.
(2025)
A numerical view on α -dissipative solutions of the Hunter- Saxton equation.
ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)
Academic article
-
Christiansen, Thomas;
Grunert, Katrin;
Nordli, Anders Samuelsen;
Solem, Susanne.
(2024)
A Convergent Numerical Algorithm for α-Dissipative Solutions of the Hunter–Saxton Equation.
Journal of Scientific Computing
Academic article
-
Grunert, Katrin.
(2024)
Uniqueness of dissipative solutions for the Camassa–Holm equation.
Journal of Differential Equations
Academic article
-
Grunert, Katrin;
Tandy, Matthew Laurence.
(2024)
A Lipschitz metric for α-dissipative solutions to the Hunter–Saxton equation.
SN Partial Differential Equations and Applications (SN PDE)
Academic article
-
Grunert, Katrin;
Reigstad, Audun.
(2023)
A regularized system for the nonlinear variational wave equation.
SN Partial Differential Equations and Applications (SN PDE)
Academic article
-
Bressan, Alberto;
Galtung, Sondre Tesdal;
Grunert, Katrin;
Nguyen, Khai Tien.
(2022)
Shock interactions for the Burgers-Hilbert equation.
Communications in Partial Differential Equations
Academic article
-
Grunert, Katrin;
Tandy, Matthew.
(2022)
Lipschitz stability for the Hunter-Saxton equation.
Journal of Hyperbolic Differential Equations
Academic article
-
Galtung, Sondre Tesdal;
Grunert, Katrin.
(2022)
Stumpons are non-conservative traveling waves of the Camassa–Holm equation.
Physica D : Non-linear phenomena
Academic article
-
Grunert, Katrin;
Holden, Helge.
(2022)
Uniqueness of conservative solutions for the Hunter–Saxton equation.
Research in the Mathematical Sciences
Academic article
-
Galtung, Sondre Tesdal;
Grunert, Katrin.
(2021)
A numerical study of variational discretizations of the Camassa–Holm equation.
BIT Numerical Mathematics
Academic article
-
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 (PNAS)
Letter to the editor
-
Grunert, Katrin;
Reigstad, Audun.
(2021)
Traveling waves for the nonlinear variational wave equation.
SN Partial Differential Equations and Applications (SN PDE)
Academic article
-
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 (PNAS)
Academic article
-
Grunert, Katrin;
Nordli, Anders Samuelsen;
Solem, Susanne.
(2021)
Numerical conservative solutions of the Hunter–-Saxton equation.
BIT Numerical Mathematics
Academic article
-
Antonio Carrillo, José;
Grunert, Katrin;
Holden, Helge.
(2020)
A Lipschitz metric for the Camassa-Holm equation.
Forum of Mathematics, Sigma
Academic article
-
Antonio Carrillo, Jose;
Grunert, Katrin;
Holden, Helge.
(2019)
A Lipschitz metric for the Hunter–Saxton equation.
Communications in Partial Differential Equations
Academic article
-
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
Academic article
-
Eckhardt, Jonathan;
Grunert, Katrin.
(2017)
A Lagrangian view on complete integrability of the conservative Camassa– Holm flow.
Journal of Integrable systems
Academic article
-
Grunert, Katrin.
(2016)
Solutions of the Camassa-Holm equation with accumulating breaking times.
Dynamics of Partial Differential Equations
Academic article
-
Grunert, Katrin;
Nguyen, Khai Tien.
(2016)
On the Burgers–Poisson equation.
Journal of Differential Equations
Academic article
-
Grunert, Katrin;
Holden, Helge.
(2016)
The general peakon-antipeakon solution for the Camassa-Holm equation.
Journal of Hyperbolic Differential Equations
Academic article
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2015)
A continuous interpolation between conservative and dissipative solutions.
Forum of Mathematics, Sigma
Academic article
-
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
Academic article
-
Grunert, Katrin.
(2015)
Blow-up for the two-component Camassa-Holm system.
Discrete and Continuous Dynamical Systems. Series A
Academic article
-
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
Academic article
-
Grunert, Katrin.
(2013)
Scattering theory for Schrodinger operators on steplike, almost periodic infinite-gap backgrounds.
Journal of Differential Equations
Academic article
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2013)
LIPSCHITZ METRIC FOR THE CAMASSA-HOLM EQUATION ON THE LINE.
Discrete and Continuous Dynamical Systems. Series A
Academic article
-
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
Academic article
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier Marcel.
(2012)
Global Solutions for the Two-Component Camassa-Holm System.
Communications in Partial Differential Equations
Academic article
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier Marcel.
(2011)
Lipschitz metric for the periodic Camassa-Holm equation.
Journal of Differential Equations
Academic article
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.
Springer Nature
Academic chapter/article/Conference paper
-
Raynaud, Xavier;
Grunert, Katrin.
(2018)
Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system.
European Mathematical Society (EMS) Press
Academic chapter/article/Conference paper
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2014)
Lipschitz metric for the two-component Camassa-Holm system.
American Institute of Mathematical Sciences (AIMS) Press
Academic chapter/article/Conference paper
-
Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2013)
Periodic conservative solutions for the two-component Camassa-Holm system.
American Mathematical Society (AMS)
Academic chapter/article/Conference paper
Report
-
Reigstad, Audun;
Grunert, Katrin;
Lindqvist, Peter;
Holden, Helge.
(2021)
A Regularized System for the Nonlinear Variational Wave Equation.
NTNU
Doctoral dissertation
-
Galtung, Sondre Tesdal;
Holden, Helge;
Grunert, Katrin;
Raynaud, Xavier.
(2020)
Discretizations of Wave Equations and Applications of Variational Principles.
NTNU
Doctoral dissertation
Teaching
Courses
Outreach
2024
-
Academic lectureGrunert, Katrin. (2024) The Camassa-Holm equation - peakons and traveling waves. Department of Mathematics and Statistics Colloquium , Florida International University 2024-02-01 - 2024-02-01
-
Academic lectureGrunert, Katrin. (2024) Uniqueness for the Camassa-Holm equation. Equadiff 2024 2024-06-10 - 2024-06-14
-
Academic lectureGrunert, Katrin. (2024) The Camassa-Holm equation - Uniqueness . 2024 CMS Summer Meeting 2024-05-31 - 2024-06-03
-
Academic lectureGrunert, Katrin. (2024) The Camassa-Holm equation - Uniqueness. Nasjonalt matematikermøte 2024 2024-09-12 - 2024-09-13
2023
-
Academic lectureGrunert, Katrin. (2023) The Hunter-Saxton equation - stability and its consequences. Institut Mittag-Leffler Water Waves and Integrable Systems 2023-09-11 - 2023-09-15
-
Academic lectureGrunert, Katrin. (2023) Numerical conservative solutions of the Hunter-Saxton equation . NumHyp23: Numerical Methods for Hyperbolic Problems 2023-06-26 - 2023-06-30
-
Academic lectureGrunert, Katrin. (2023) Shock interactions for the Burgers-Hilbert equation. 29th Nordic Congress of Mathematicians 2023-07-03 - 2023-07-07
2022
-
Academic lectureGrunert, Katrin. (2022) Uniqueness of conservative solutions for the Hunter-Saxton equation. 18th International Conference on Hyperbolic Problems: Theory, Numerics, Applications 2022-06-20 - 2022-06-24
-
Academic lectureGrunert, Katrin. (2022) Traveling waves for nonlinear wave equations. Norwegian meeting on PDEs 2022-06-08 - 2022-06-10
-
Academic lectureGrunert, Katrin. (2022) Traveling waves for nonlinear wave equations. 28th Nordic Congress of Mathematicians 2022-08-18 - 2022-08-21
2021
-
Academic lectureGrunert, Katrin. (2021) Traveling waves for nonlinear wave equations. PDEA Webinar 2021-12-09 - 2021-12-09
2020
-
Academic lectureGrunert, Katrin. (2020) Lipschitz metrics for nonlinear PDEs. DMV Jahrestagung 2020 2020-09-14 - 2020-09-17
2019
-
Academic lectureGrunert, Katrin. (2019) Lipschitz metrics for nonlinear PDEs. Norwegian meeting on PDEs , Trondheim 2019-06-05 - 2019-06-07
-
Academic lectureGrunert, Katrin. (2019) Lipschitz metrics for nonlinear PDEs. Guiseppe Saccomandi, Perugia Yasemin Sengül, Istanbul Luigi Mini-Workshop on Mathematical Aspects of Nonlinear Wave Propagation in Solid Mechanics , Mathematisches Forschungsinstitut Oberwolfach 2019-03-03 - 2019-03-09
2018
-
Academic lectureGrunert, Katrin. (2018) Lipschitz metrics for the Hunter–Saxton equation. Summer school on Nonlocal Interactions in Partial Differential Equations and Geometry 2018-05-21 - 2018-05-25
-
Academic lectureGrunert, Katrin. (2018) Lipschitz metrics for a nonlinear PDE. TU München GAMM Annual Meeting 2018 , München 2018-03-19 - 2018-03-23
-
Academic lectureGrunert, Katrin. (2018) Lipschitz metrics for nonlinear PDEs. 17th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP 2018) 2018-06-25 - 2018-06-29
2017
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Academic lectureGrunert, Katrin. (2017) Lipschitz metrics for nonlinear PDEs. Workshop on Hyperbolic Problems 2017-10-26 - 2017-10-26
-
Academic lectureGrunert, Katrin. (2017) Lipschitz metrics for nonlinear PDEs. Workshop on Aggregation-Diffusion PDEs: Variational Principles, Nonlocality and Systems 2017-07-10 - 2017-07-14
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Academic lectureGrunert, Katrin. (2017) A Lipschitz metric for the Hunter–Saxton equation. Workshop on PDEs: Modelling, Analysis and Numerical Simulation (PDE-MANS 2017) 2017-06-19 - 2017-06-23
2016
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Academic lectureGrunert, Katrin. (2016) Blow-up for the two-component Camassa-Holm system. Non-linear PDEs, mathematical physics, and stochastic analysis - A conference in honour of Helge Holden 2016-07-04 - 2016-07-07
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Academic lectureGrunert, Katrin. (2016) Blow-up for the two-component Camassa-Holm system. 16th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP 2016) 2016-08-01 - 2016-08-05
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Academic lectureGrunert, Katrin. (2016) Stability for weak solution of the Hunter–Saxton equation. Seminar 2016-10-13 - 2016-10-13
2014
-
Academic lectureNordli, Anders Samuelsen; Grunert, Katrin. (2014) Lipschitz metric for the dissipative Hunter-Saxton system. 15th international conference on hyperbolic problems: Theory, numerics, applications , Rio de Janeiro 2014-07-27 - 2014-08-01