Blar i NTNU Open på forfatter "Grunert, Katrin"
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Shock interactions for the Burgers-Hilbert equation
Bressan, Alberto; Galtung, Sondre Tesdal; Grunert, Katrin; Nguyen, Khai Tien (Peer reviewed; Journal article, 2022)This paper provides an asymptotic description of a solution to the Burgers-Hilbert equation in a neighborhood of a point where two shocks interact. The solution is obtained as the sum of a function with H2 regularity away ... -
Solutions of the Camassa-Holm equation with accumulating breaking times
Grunert, Katrin (Journal article, 2016)We present two initial profiles to the Camassa–Holm equation which yield solutions with accumulating breaking times -
Stability of solutions to the Hunter-Saxton equation and well-posedness of coupled problems
Tandy, Matthew (Doctoral theses at NTNU;2023:239, Doctoral thesis, 2023) -
Stumpons are non-conservative traveling waves of the Camassa–Holm equation
Galtung, Sondre Tesdal; Grunert, Katrin (Peer reviewed; Journal article, 2022)It is well-known that by requiring solutions of the Camassa–Holm equation to satisfy a particular local conservation law for the energy in the weak sense, one obtains what is known as conservative solutions. As conservative ... -
Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system
Raynaud, Xavier; Grunert, Katrin (Chapter, 2018)Compared with the two-component Camassa–Holm system, the modified two-component Camassa–Holm system introduces a regularized density which makes possible the existence of solutions of lower regularity, and in particular ... -
The general peakon-antipeakon solution for the Camassa-Holm equation
Grunert, Katrin; Holden, Helge (Journal article; Peer reviewed, 2016)We compute explicitly the peakon-antipeakon solution of the Camassa– Holm equation ut − utxx + 3uux − 2uxuxx − uuxxx = 0 in the non-symmetric and α-dissipative case. The solution experiences wave breaking in finite time, ... -
Traveling Wave Solutions for the Hunter-Saxton Equation
Christiansen, Thomas (Master thesis, 2021)I denne oppgaven studerer vi vandrende bølgeløsninger for Hunter-Saxton likningen. Vi benytter en lime-formalisme som lar oss lime sammen to klassiske vandrende løsninger langs en kurve. Dette lar oss konstruere svake ... -
Traveling waves for the nonlinear variational wave equation
Grunert, Katrin; Reigstad, Audun (Peer reviewed; Journal article, 2021)We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of ... -
Uniqueness of conservative solutions for the Hunter–Saxton equation
Grunert, Katrin; Holden, Helge (Peer reviewed; Journal article, 2022)We show that the Hunter–Saxton equation ut+uux=14(∫x−∞dμ(t,z)−∫∞xdμ(t,z)) and μt+(uμ)x=0 has a unique, global, weak, and conservative solution (u,μ) of the Cauchy problem on the line.