Katrin Grunert
Associate 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:

Spring 2017: TMA4165 Differential Equations and Dynamical Systems
Spring 2016: TMA4165 Differential Equations and Dynamical Systems
Fall 2015: TMA4120 Matematikk 4K
Fall 2014: TMA4120 Matematikk 4K
Spring 2014: MA1202 Linear Algebra and Applications



Projects:

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:

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

On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system, together with M. Grasmair and H. Holden, pdf.

A Lipschitz metric for the Hunter-Saxton equation, together with J.A. Carrillo and H. Holden, pdf.

Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter-Saxton system, together with A. Nordli, pdf.


Publications:


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

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

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

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

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), pdf.

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

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, pdf.

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), pdf.

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, pdf.

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

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), pdf.

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

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), pdf.

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

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

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), pdf.

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), pdf.



Doctoral thesis:

Scattering Theory and Cauchy Problems, Advisor: Gerald Teschl at the Faculty of Mathematics at the University of Vienna, pdf.



Diploma thesis:

Long-time Asymptotics for the KdV Equation, Advisor: Gerald Teschl at the Faculty of Mathematics at the University of Vienna, pdf.



Note that these files are for personal use only. If you have problems reading these files feel free to contact me.




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