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.
- Workshop Wave Phenomena and Stability, 3.-5. September 2024
- Participant in the RCN Toppforsk project Waves and Nonlinear Phenomena, 2016-2022.
I am currently supervising 1 PhD student and mentoring 1 PostDoc.
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
- T. Christiansen and K. Grunert, A numerical view on α-dissipative solutions of the Hunter-Saxton equation, arXiv:2404.11174.
- T. Christiansen and K. Grunert, Rate of convergence for numerical α-dissipative solutions of the Hunter-Saxton equation, arXiv:2411.07712.
2024
-
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
-
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
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
-
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
-
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
2021
-
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
-
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
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;
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
-
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;
Reigstad, Audun.
(2023)
A regularized system for the nonlinear variational wave equation.
SN Partial Differential Equations and Applications (SN PDE)
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
-
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
-
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
-
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
-
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