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: 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 regularized system for the nonlinear variational wave equation, together with A. Reigstad, arXiv.



Publications:


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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



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