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 nonlinear 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, 20192024.
 Participant in the RCN Toppforsk project Waves and Nonlinear Phenomena, 20162022.
I am currently supervising 1 PhD student and mentoring 1 PostDoc.
Research
My research focuses on nonlinear 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, 20192023.
 Participant in the RCN Toppforsk project Waves and Nonlinear Phenomena, 20162022.
I am currently supervising 2 PhD students and mentoring 1 PostDoc.
Publications
Preprints
 T. Christiansen and K. Grunert, A numerical view on αdissipative solutions of the HunterSaxton equation, arXiv:2404.11174.
 K. Grunert, Uniqueness of dissipative solutions for the CamassaHolm Equation, arXiv:2311.15344.
2024

Grunert, Katrin;
Tandy, Matthew Laurence.
(2024)
A Lipschitz metric for αdissipative 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 αDissipative Solutions of the Hunter–Saxton Equation.
Journal of Scientific Computing
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 BurgersHilbert equation.
Communications in Partial Differential Equations
Academic article

Grunert, Katrin;
Tandy, Matthew.
(2022)
Lipschitz stability for the HunterSaxton equation.
Journal of Hyperbolic Differential Equations
Academic article

Galtung, Sondre Tesdal;
Grunert, Katrin.
(2022)
Stumpons are nonconservative traveling waves of the Camassa–Holm equation.
Physica D : Nonlinear 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

Grunert, Katrin;
Nordli, Anders Samuelsen;
Solem, Susanne.
(2021)
Numerical conservative solutions of the Hunter–Saxton 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
Letter to the editor

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
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;
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
2020

Antonio Carrillo, José;
Grunert, Katrin;
Holden, Helge.
(2020)
A Lipschitz metric for the CamassaHolm 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

Raynaud, Xavier;
Grunert, Katrin.
(2018)
Symmetries and multipeakon solutions for the modified twocomponent CamassaHolm system.
European Mathematical Society (EMS) Press
Academic chapter/article/Conference paper

Grunert, Katrin;
Nordli, Anders Samuelsen.
(2018)
Existence and Lipschitz stability for αdissipative solutions of the twocomponent Hunter–Saxton system.
Journal of Hyperbolic Differential Equations
Academic article

Grunert, Katrin;
Holden, Helge;
Grasmair, Markus.
(2018)
On the Equivalence of Eulerian and Lagrangian Variables for the TwoComponent Camassa–Holm System.
Springer Nature
Academic chapter/article/Conference paper
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 CamassaHolm 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 peakonantipeakon solution for the CamassaHolm 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.
(2015)
Blowup for the twocomponent CamassaHolm system.
Discrete and Continuous Dynamical Systems. Series A
Academic article

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2015)
A continuous interpolation between conservative and dissipative solutions for the twocomponent CamassaHolm system.
Forum of Mathematics, Sigma
Academic article
2014

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2014)
Global dissipative solutions of the twocomponent CamassaHolm system for initial data with nonvanishing asymptotics.
Nonlinear Analysis: Real world applications
Academic article

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2014)
Lipschitz metric for the twocomponent CamassaHolm system.
American Institute of Mathematical Sciences (AIMS) Press
Academic chapter/article/Conference paper
2013

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2013)
Periodic conservative solutions for the twocomponent CamassaHolm system.
American Mathematical Society (AMS)
Academic chapter/article/Conference paper

Grunert, Katrin.
(2013)
Scattering theory for Schrodinger operators on steplike, almost periodic infinitegap backgrounds.
Journal of Differential Equations
Academic article

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2013)
LIPSCHITZ METRIC FOR THE CAMASSAHOLM 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 CAMASSAHOLM 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 TwoComponent CamassaHolm System.
Communications in Partial Differential Equations
Academic article
2011

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier Marcel.
(2011)
Lipschitz metric for the periodic CamassaHolm equation.
Journal of Differential Equations
Academic article
Journal publications

Grunert, Katrin;
Tandy, Matthew Laurence.
(2024)
A Lipschitz metric for αdissipative 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 αDissipative Solutions of the Hunter–Saxton Equation.
Journal of Scientific Computing
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 BurgersHilbert equation.
Communications in Partial Differential Equations
Academic article

Grunert, Katrin;
Tandy, Matthew.
(2022)
Lipschitz stability for the HunterSaxton equation.
Journal of Hyperbolic Differential Equations
Academic article

Galtung, Sondre Tesdal;
Grunert, Katrin.
(2022)
Stumpons are nonconservative traveling waves of the Camassa–Holm equation.
Physica D : Nonlinear phenomena
Academic article

Grunert, Katrin;
Holden, Helge.
(2022)
Uniqueness of conservative solutions for the Hunter–Saxton equation.
Research in the Mathematical Sciences
Academic article

Grunert, Katrin;
Nordli, Anders Samuelsen;
Solem, Susanne.
(2021)
Numerical conservative solutions of the Hunter–Saxton 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
Letter to the editor

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
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;
Reigstad, Audun.
(2021)
Traveling waves for the nonlinear variational wave equation.
SN Partial Differential Equations and Applications (SN PDE)
Academic article

Antonio Carrillo, José;
Grunert, Katrin;
Holden, Helge.
(2020)
A Lipschitz metric for the CamassaHolm 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 αdissipative solutions of the twocomponent 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 CamassaHolm 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 peakonantipeakon solution for the CamassaHolm 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.
(2015)
Blowup for the twocomponent CamassaHolm system.
Discrete and Continuous Dynamical Systems. Series A
Academic article

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2015)
A continuous interpolation between conservative and dissipative solutions for the twocomponent CamassaHolm system.
Forum of Mathematics, Sigma
Academic article

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2014)
Global dissipative solutions of the twocomponent CamassaHolm 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 infinitegap backgrounds.
Journal of Differential Equations
Academic article

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2013)
LIPSCHITZ METRIC FOR THE CAMASSAHOLM 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 CAMASSAHOLM 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 TwoComponent CamassaHolm System.
Communications in Partial Differential Equations
Academic article

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier Marcel.
(2011)
Lipschitz metric for the periodic CamassaHolm equation.
Journal of Differential Equations
Academic article
Part of book/report

Raynaud, Xavier;
Grunert, Katrin.
(2018)
Symmetries and multipeakon solutions for the modified twocomponent CamassaHolm system.
European Mathematical Society (EMS) Press
Academic chapter/article/Conference paper

Grunert, Katrin;
Holden, Helge;
Grasmair, Markus.
(2018)
On the Equivalence of Eulerian and Lagrangian Variables for the TwoComponent Camassa–Holm System.
Springer Nature
Academic chapter/article/Conference paper

Grunert, Katrin;
Holden, Helge;
Raynaud, Xavier.
(2014)
Lipschitz metric for the twocomponent CamassaHolm 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 twocomponent CamassaHolm 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
Knowledge Transfer
2024

Academic lectureGrunert, Katrin. (2024) The CamassaHolm equation  peakons and traveling waves. Department of Mathematics and Statistics Colloquium , Florida International University 20240201  20240201

Academic lectureGrunert, Katrin. (2024) Uniqueness for the CamassaHolm equation. Equadiff 2024 20240610  20240614

Academic lectureGrunert, Katrin. (2024) The CamassaHolm equation  Uniqueness . 2024 CMS Summer Meeting 20240531  20240603
2023

Academic lectureGrunert, Katrin. (2023) Numerical conservative solutions of the HunterSaxton equation . NumHyp23: Numerical Methods for Hyperbolic Problems 20230626  20230630

Academic lectureGrunert, Katrin. (2023) Shock interactions for the BurgersHilbert equation. 29th Nordic Congress of Mathematicians 20230703  20230707

Academic lectureGrunert, Katrin. (2023) The HunterSaxton equation  stability and its consequences. Institut MittagLeffler Water Waves and Integrable Systems 20230911  20230915
2022

Academic lectureGrunert, Katrin. (2022) Uniqueness of conservative solutions for the HunterSaxton equation. 18th International Conference on Hyperbolic Problems: Theory, Numerics, Applications 20220620  20220624

Academic lectureGrunert, Katrin. (2022) Traveling waves for nonlinear wave equations. Norwegian meeting on PDEs 20220608  20220610

Academic lectureGrunert, Katrin. (2022) Traveling waves for nonlinear wave equations. 28th Nordic Congress of Mathematicians 20220818  20220821
2021

Academic lectureGrunert, Katrin. (2021) Traveling waves for nonlinear wave equations. PDEA Webinar 20211209  20211209
2020

Academic lectureGrunert, Katrin. (2020) Lipschitz metrics for nonlinear PDEs. DMV Jahrestagung 2020 20200914  20200917
2019

Academic lectureGrunert, Katrin. (2019) Lipschitz metrics for nonlinear PDEs. Norwegian meeting on PDEs , Trondheim 20190605  20190607

Academic lectureGrunert, Katrin. (2019) Lipschitz metrics for nonlinear PDEs. Guiseppe Saccomandi, Perugia Yasemin Sengül, Istanbul Luigi MiniWorkshop on Mathematical Aspects of Nonlinear Wave Propagation in Solid Mechanics , Mathematisches Forschungsinstitut Oberwolfach 20190303  20190309
2018

Academic lectureGrunert, Katrin. (2018) Lipschitz metrics for the Hunter–Saxton equation. Summer school on Nonlocal Interactions in Partial Differential Equations and Geometry 20180521  20180525

Academic lectureGrunert, Katrin. (2018) Lipschitz metrics for a nonlinear PDE. TU München GAMM Annual Meeting 2018 , München 20180319  20180323

Academic lectureGrunert, Katrin. (2018) Lipschitz metrics for nonlinear PDEs. 17th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP 2018) 20180625  20180629
2017

Academic lectureGrunert, Katrin. (2017) Lipschitz metrics for nonlinear PDEs. Workshop on AggregationDiffusion PDEs: Variational Principles, Nonlocality and Systems 20170710  20170714

Academic lectureGrunert, Katrin. (2017) Lipschitz metrics for nonlinear PDEs. Workshop on Hyperbolic Problems 20171026  20171026

Academic lectureGrunert, Katrin. (2017) A Lipschitz metric for the Hunter–Saxton equation. Workshop on PDEs: Modelling, Analysis and Numerical Simulation (PDEMANS 2017) 20170619  20170623
2016

Academic lectureGrunert, Katrin. (2016) Stability for weak solution of the Hunter–Saxton equation. Seminar 20161013  20161013

Academic lectureGrunert, Katrin. (2016) Blowup for the twocomponent CamassaHolm system. Nonlinear PDEs, mathematical physics, and stochastic analysis  A conference in honour of Helge Holden 20160704  20160707

Academic lectureGrunert, Katrin. (2016) Blowup for the twocomponent CamassaHolm system. 16th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP 2016) 20160801  20160805
2014

Academic lectureNordli, Anders Samuelsen; Grunert, Katrin. (2014) Lipschitz metric for the dissipative HunterSaxton system. 15th international conference on hyperbolic problems: Theory, numerics, applications , Rio de Janeiro 20140727  20140801