index

Katrin Grunert
Professor
Institutt for matematiske fag
Norges teknisk-naturvitenskapelige universitet (NTNU)
Alfred Getz vei 1
NO-7491 Trondheim
Norway
Office: Sentralbygg 2, Rom 1150
Phone: +47 735 93537
E-mail: katrin.grunert@ntnu.no

Teaching:

Fall 2022: TMA4305 Partial Differential Equations
Fall 2018, 2019, 2020: MA1201 Linear Algebra and Geometry
Fall 2017: TMA4100 Matematikk 1
Spring 2016, 2017, 2018, 2023, 2024: TMA4165 Differential Equations and Dynamical Systems
Fall 2014, 2015: TMA4120 Matematikk 4K
Spring 2014: MA1202 Linear Algebra and Applications

Projects:

WaPheS (Wave Phenomena and Stability - a Shocking Combination) is a four-year project aiming to analyze how nonlinear terms affect the stability of global solution concepts for partial differential equations that model wave phenomena.

WaNP (Waves and Nonlinear Phenomena) is a five-year project aiming to analyze the interplay of singularities and nonlocal effects in the solutions of partial differential equations that model wave phenomena.

Preprints:

T. Christiansen and K. Grunert: A numerical view on α-dissipative solutions of the Hunter-Saxton equation, arXiv.

K. Grunert: Uniqueness of dissipative solutions for the Camassa-Holm equation, arXiv.

K. Grunert, M. Tandy: A Lipschitz metric for α-dissipative solutions to the Hunter-Saxton equation, arXiv.

Publications:

T. Christiansen, K. Grunert, A. Nordli, and S. Solem: A numerical algorithm for α-dissipative solutions of the Hunter-Saxton equation, J. Sci. Comput. 99, 44 (2024), DOI, arXiv.

K. Grunert, A. Reigstad: A regularized system for the nonlinear variational wave equation, Partial Differ. Equ. Appl. 4, 35 (2023), DOI, arXiv.

A. Bressan, S. T. Galtung, K. Grunert, K. T. Nguyen: Shock interactions for the Burgers-Hilbert equation, Comm. Partial Differential Equations 47, 1795-1844 (2022), DOI, arXiv.

K. Grunert, M. Tandy: Lipschitz stability for the Hunter-Saxton equation, J. Hyperbolic Differ. Equ. 19, 275-310 (2022), DOI, arXiv.

K. Grunert, H. Holden: Uniqueness of conservative solutions for the Hunter-Saxton equation, Res. Math. Sci. 9, 19 (2022), DOI, arXiv.

S. T. Galtung, K. Grunert: Stumpons are non-conservative traveling waves of the Camassa-Holm equation, Phys. D 433, 133196 (2022), DOI, arXiv.

S. T. Galtung, K. Grunert: A numerical study of variational discretizations of the Camassa-Holm equation, BIT 61, 1271-1309 (2021), DOI, arXiv.

K. Grunert, A. Reigstad: Traveling waves for the nonlinear variational wave equation, Partial Differ. Equ. Appl. 2, 61 (2021), DOI, arXiv.

K. Grunert, A. Nordli, S. Solem: Numerical conservative solutions of the Hunter-Saxton equation, BIT 61, 441-471 (2021), DOI, arXiv.

J. A. Carrillo, K. Grunert, H. Holden: A Lipschitz metric for the Camassa-Holm equation, Forum Math. Sigma 8, e27, 292 pages (2020), DOI, arXiv.

J. A. Carrillo, K. Grunert, H. Holden: A Lipschitz metric for the Hunter-Saxton equation, Comm. Partial Differential Equations 44, 309-334 (2019), DOI, arXiv.

K. Grunert, A. Nordli: Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter-Saxton system, J. Hyper. Differential Equations 15, 559-597 (2018), DOI, arXiv.

M. Grasmair, K. Grunert, H. Holden: On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system, in Current Research in Nonlinear Analysis, T.M. Rassias (ed), 157-201, Springer Optim. Appl. 135, Springer, Cham, 2018, DOI, arXiv.

K. Grunert, X. Raynaud: Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system, in Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis, F. Gesztesy et al. (eds), 227-260, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2018, DOI, arXiv.

J. Eckhardt, K. Grunert: A Lagrangian view on complete integrability of the two-component Camassa-Holm system, J. Integrable Syst. 2, xyx002 (2017), DOI, arXiv.

K. Grunert, K. T. Nguyen: On the Burgers-Poisson equation, J. Differential Equations 261, 3220-3246 (2016), DOI, arXiv.

K. Grunert, H. Holden: The general peakon-antipeakon solution for the Camassa-Holm equation, J. Hyper. Differential Equations 13, 353-380 (2016), DOI, arXiv.

K. Grunert: Solutions of the Camassa-Holm equation with accumulating breaking times, Dynamics of PDE 13, 91-105 (2016), DOI, arXiv.

K. Grunert, H. Holden, X. Raynaud: A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system , Forum Math. Sigma 3, e1, 73 pages (2015), DOI, arXiv.

K. Grunert: Blow-up for the two-component Camassa-Holm system, Discrete Contin. Dyn. Syst. 35, 2041-2051 (2015), DOI, arXiv.

K. Grunert, H. Holden, X. Raynaud: Lipschitz metric for the two-component Camassa-Holm system, in Hyperbolic Problems: Theory, Numerics, Applications, F. Ancona et al. (eds), 193-207, AIMS on Applied Mathematics 8, AIMS 2014, arXiv.

K. Grunert, H. Holden, X. Rauynaud: Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics, Nonlinear Anal. Real World Appl. 17, 203-244 (2014), DOI, arXiv.

K. Grunert, H. Holden, X. Raynaud: Periodic conservative solutions for the two-component Camassa-Holm system, in Spectral Analysis, Differential Equations and Mathematical Physics, H. Holden et al. (eds), 165-182, Proc. Symp. Pure Math., Amer. Math. Soc. 87, Providence, 2013, DOI, arXiv.

K. Grunert: Scattering theory for Schrödinger operators on steplike, almost periodic infinite-gap backgrounds, J. Differential Equations 254, 2556-2586 (2013), DOI, arXiv.

K. Grunert, H. Holden, X. Raynaud: Lipschitz metric for the Camassa-Holm equation on the line, Discrete Contin. Dyn. Syst. 33, 2809-2827 (2013), DOI, arXiv.

K. Grunert, H. Holden, X. Raynaud: Global solutions for the two-component Camassa-Holm system, Comm. Partial Differential Equations 37, 2245-2271 (2012), DOI, arXiv.

K. Grunert, H. Holden, X. Raynaud: Global conservative solutions to the Camassa-Holm equation for initial data with nonvanishing asymptotics, Discrete Contin. Dyn. Syst. 32, 4209-4227 (2012), DOI, arXiv.

K. Grunert: The transformation operator for Schrödinger operators on almost periodic infinite-gap backgrounds, J. Differential Equations 250, 3534-3558 (2011), DOI, arXiv.

K. Grunert, H. Holden, X. Raynaud: Lipschitz metric for the periodic Camassa-Holm equation, J. Differential Equations 250, 1460-1492 (2011), DOI, arXiv.

K. Grunert, G. Teschl: Long-time asymptotics for the Korteweg-de Vries equation via nonlinear steepest descent, Math. Phys. Anal. Geom. 12, 287-324 (2009), DOI, arXiv.

I. Egorova, K. Grunert, G. Teschl: On the Cauchy problem for the Korteweg-de Vries equation with steplike, finite-gap initial data I. Schwartz type perturbations, Nonlinearity 22, 1431-1457 (2009), DOI, arXiv.

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