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 2018, 2019: MA1201 Linear Algebra and Geometry
Fall 2017: TMA4100 Matematikk 1
Spring 2016, 2017, 2018: 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:


A Lipschitz metric for the Camassa-Holm equation, together with J.A. Carrillo and H. Holden, arXiv.



Publications:


A Lipschitz metric for the Hunter-Saxton equation, together with J.A. Carrillo and H. Holden, Comm. Partial Differential Equations 44, 309-334 (2019), arXiv.

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

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

Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system, together with X. Raynaud, 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, arXiv.

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

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

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

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

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

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

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

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

Periodic conservative solutions for the two-component Camassa-Holm system, together with H. Holden and X. Raynaud, 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, arXiv.

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

Lipschitz metric for the Camassa-Holm equation on the line, together with H. Holden and X. Raynaud, Discrete Contin. Dyn. Syst. 33, 2809-2827 (2013), arXiv.

Global solutions for the two-component Camassa-Holm system, together with H. Holden and X. Raynaud, Comm. Partial Differential Equations 37, 2245-2271 (2012), arXiv.

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

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

Lipschitz metric for the periodic Camassa-Holm equation, together with H. Holden and X. Raynaud, J. Differential Equations 250, 1460-1492 (2011), arXiv.

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

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



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