Browsing NTNU Open by Author "Grunert, Katrin"
Now showing items 1-20 of 31
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A Lagrangian view on complete integrability of the conservative Camassa– Holm flow
Eckhardt, Jonathan; Grunert, Katrin (Journal article; Peer reviewed, 2017)We show how the change from Eulerian to Lagrangian coordinates for the two-component Camassa–Holm system can be understood in terms of certain reparametrizations of the underlying isospectral problem. The respective ... -
A Lipschitz metric for the Hunter–Saxton equation
Antonio Carrillo, Jose; Grunert, Katrin; Holden, Helge (Journal article; Peer reviewed, 2019)We analyze stability of conservative solutions of the Cauchy problem on the line for the (integrated) Hunter–Saxton (HS) equation. Generically, the solutions of the HS equation develop singularities with steep gradients ... -
Analysis and discretization of fractional Mean Field Games
Ersland, Olav (Doctoral theses at NTNU;2021:399, Doctoral thesis, 2021) -
A continuous interpolation between conservative and dissipative solutions
Grunert, Katrin; Holden, Helge; Raynaud, Xavier (Peer reviewed; Journal article, 2015)We introduce a novel solution concept, denoted -dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system ... -
A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system
Grunert, Katrin; Holden, Helge; Raynaud, Xavier (Peer reviewed; Journal article, 2015)We introduce a novel solution concept, denotedα-dissipative solutions, that provides a continuousinterpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system ... -
A Convergent Numerical Algorithm for α-Dissipative Solutions of the Hunter–Saxton Equation
Christiansen, Thomas; Grunert, Katrin; Nordli, Anders Samuelsen; Solem, Susanne (Peer reviewed; Journal article, 2024)A convergent numerical method for -dissipative solutions of the Hunter–Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the ... -
Discretizations of Wave Equations and Applications of Variational Principles
Galtung, Sondre Tesdal (Doctoral theses at NTNU;2020:331, Doctoral thesis, 2020) -
Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig–MacArthur predator–prey model
Grunert, Katrin; Holden, Helge; Jakobsen, Espen Robstad; Stenseth, Nils Christian (Peer reviewed; Journal article, 2021)An evolutionarily stable strategy (ESS) is an evolutionary strategy that, if adapted by a population, cannot be invaded by any deviating (mutant) strategy. The concept of ESS has been extensively studied and widely applied ... -
Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter–Saxton system
Grunert, Katrin; Nordli, Anders Samuelsen (Journal article, 2018)We establish the concept of α-dissipative solutions for the two-component Hunter–Saxton system under the assumption that either α(x)=1 or 0≤α(x)<1 for all x∈R. Furthermore, we investigate the Lipschitz stability of solutions ... -
Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics
Grunert, Katrin; Holden, Helge; Raynaud, Xavier (Journal article, 2014)We show the existence of a global weak dissipative solution of the Cauchy problem for the two-component Camassa–Holm (2CH) system on the line with nonvanishing and distinct spatial asymptotics. The influence from the second ... -
A Lipschitz metric for the Camassa--Holm equation
Antonio Carrillo, José; Grunert, Katrin; Holden, Helge (Peer reviewed; Journal article, 2020)We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving ... -
A Lipschitz metric for ⍺-dissipative solutions to the Hunter-Saxton equation
Grunert, Katrin; Tandy, Matthew Laurence (Journal article; Peer reviewed, 2024)We explore the Lipschitz stability of solutions to the Hunter–Saxton equation with respect to the initial data. In particular, we study the stability of α-dissipative solutions constructed using a generalised method of ... -
Lipschitz stability for the Hunter-Saxton equation
Grunert, Katrin; Tandy, Matthew (Journal article, 2022) -
Numerical conservative solutions of the Hunter–-Saxton equation
Grunert, Katrin; Nordli, Anders Samuelsen; Solem, Susanne (Peer reviewed; Journal article, 2021)In the article a convergent numerical method for conservative solutions of the Hunter–Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the ... -
A numerical study of variational discretizations of the Camassa–Holm equation
Galtung, Sondre Tesdal; Grunert, Katrin (Peer reviewed; Journal article, 2021)We present two semidiscretizations of the Camassa–Holm equation in periodic domains based on variational formulations and energy conservation. The first is a periodic version of an existing conservative multipeakon method ... -
On the Burgers–Poisson equation
Grunert, Katrin; Nguyen, Khai Tien (Journal article, 2016)In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L 1 (R). In addition an Oleinik type estimate is established and some criteria on local ... -
On the Equivalence of Eulerian and Lagrangian Variables for the Two-Component Camassa–Holm System
Grunert, Katrin; Holden, Helge; Grasmair, Markus (Chapter, 2018)The Camassa–Holm equation and its two-component Camassa–Holm system generalization both experience wave breaking in finite time. To analyze this, and to obtain solutions past wave breaking, it is common to reformulate the ... -
On the two-component Hunter–Saxton system
Nordli, Anders (Doctoral theses at NTNU;2017:146, Doctoral thesis, 2017)In 1991 Hunter and Saxton introduced a novel equation related to the dynamics of liquid crystals. The equation exhibited startling properties, among them wave breaking in finite time. Here we study the effects of ... -
A Regularized System for the Nonlinear Variational Wave Equation
Reigstad, Audun (Doctoral theses at NTNU;2021:21, Doctoral thesis, 2021) -
A regularized system for the nonlinear variational wave equation
Grunert, Katrin; Reigstad, Audun (Peer reviewed; Journal article, 2023)We present a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.