Search Results - "Grunert, Katrin"

A numerical study of variational discretizations of the Camassa–Holm equation by Galtung, Sondre Tesdal, Grunert, Katrin

“…We present two semidiscretizations of the Camassa–Holm equation in periodic domains based on variational formulations and energy conservation. The first is a…”
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Uniqueness of conservative solutions for the Hunter–Saxton equation by Grunert, Katrin, Holden, Helge

“…We show that the Hunter–Saxton equation u t + u u x = 1 4 ( ∫ - ∞ x d μ ( t , z ) - ∫ x ∞ d μ ( t , z ) ) and μ t + ( u μ ) x = 0 has a unique, global, weak,…”
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Long-Time Asymptotics for the Korteweg–de Vries Equation via Nonlinear Steepest Descent by Grunert, Katrin, Teschl, Gerald

“…We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg–de Vries equation for decaying initial data in the…”
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Numerical conservative solutions of the Hunter–Saxton equation by Grunert, Katrin, Nordli, Anders, Solem, Susanne

“…In the article a convergent numerical method for conservative solutions of the Hunter–Saxton equation is derived. The method is based on piecewise linear…”
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Global Solutions for the Two-Component Camassa-Holm System by Grunert, Katrin, Holden, Helge, Raynaud, Xavier

“…We prove existence of a global conservative solution of the Cauchy problem for the two-component Camassa-Holm (2CH) system on the line, allowing for…”
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A LIPSCHITZ METRIC FOR THE CAMASSA–HOLM EQUATION by CARRILLO, JOSÉ A., GRUNERT, KATRIN, HOLDEN, HELGE

“…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…”
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Uniqueness of dissipative solutions for the Camassa–Holm equation by Grunert, Katrin

“…We show that the Cauchy problem for the Camassa–Holm equation has a unique, global, weak, and dissipative solution for any initial data u0∈H1(R), such that…”
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A CONTINUOUS INTERPOLATION BETWEEN CONSERVATIVE AND DISSIPATIVE SOLUTIONS FOR THE TWO-COMPONENT CAMASSA–HOLM SYSTEM by GRUNERT, KATRIN, HOLDEN, HELGE, RAYNAUD, XAVIER

“…We introduce a novel solution concept, denoted ${\it\alpha}$-dissipative solutions, that provides a continuous interpolation between conservative and…”
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Stumpons are non-conservative traveling waves of the Camassa–Holm equation by Galtung, Sondre Tesdal, Grunert, Katrin

“…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…”
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Scattering theory for Schrödinger operators on steplike, almost periodic infinite-gap backgrounds by Grunert, Katrin

“…We develop direct scattering theory for one-dimensional Schrödinger operators with steplike potentials, which are asymptotically close to different Bohr almost…”
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A Lipschitz metric for the Hunter-Saxton equation by Antonio Carrillo, José, Grunert, Katrin, Holden, Helge

“…We analyze stability of conservative solutions of the Cauchy problem on the line for the (integrated) Hunter-Saxton (HS) equation. Generically, the solutions…”
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Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig–MacArthur predator–prey model by Grunert, Katrin, Holden, Helge, Jakobsen, Espen R., Stenseth, Nils Chr

“…An evolutionarily stable strategy (ESS) is an evolutionary strategy that, if adapted by a population, cannot be invaded by any deviating (mutant) strategy. The…”
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The transformation operator for Schrödinger operators on almost periodic infinite-gap backgrounds by Grunert, Katrin

“…We investigate the kernels of the transformation operators for one-dimensional Schrödinger operators with potentials, which are asymptotically close to Bohr…”
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A Convergent Numerical Algorithm for α-Dissipative Solutions of the Hunter–Saxton Equation by Christiansen, Thomas, Grunert, Katrin, Nordli, Anders, Solem, Susanne

“…A convergent numerical method for α -dissipative solutions of the Hunter–Saxton equation is derived. The method is based on applying a tailor-made projection…”
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REPLY TO BEST AND ASHBY: The concept of evolutionarily stable strategies (ESS) helps link ecology and evolution by Grunert, Katrin, Holden, Helge, Jakobsen, Espen R., Stenseth, Nils Chr

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Shock interactions for the Burgers-Hilbert equation by Bressan, Alberto, Galtung, Sondre T., Grunert, Katrin, Nguyen, Khai T.

“…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…”
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Global dissipative solutions of the two-component Camassa–Holm system for initial data with nonvanishing asymptotics by Grunert, Katrin, Holden, Helge, Raynaud, Xavier

“…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…”
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Uniqueness of dissipative solutions for the Camassa-Holm equation by Grunert, Katrin

“…J. Differential Equations 412, 474-528 (2024) We show that the Cauchy problem for the Camassa-Holm equation has a unique, global, weak, and dissipative…”
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A Lagrangian View on Complete Integrability of the Two-Component Camassa–Holm System by Eckhardt, Jonathan, Grunert, Katrin

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Lipschitz metric for the periodic Camassa–Holm equation by Grunert, Katrin, Holden, Helge, Raynaud, Xavier

“…We study the stability of conservative solutions of the Cauchy problem for the Camassa–Holm equation u t − u x x t + κ u x + 3 u u x − 2 u x u x x − u u x x x…”
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