9 citations · 32 across the 12 of their papers we have counts for
13 papers
Wave breaking for the nonlinear variational wave equation
Sondre Tesdal Galtung, Katrin Grunert
Following conservative solutions of the nonlinear variational wave equation along forward and backward characteristics, we identify criteria, which guara…
The sticky particle dynamics of the 1D pressureless Euler-alignment system as a gradient flow
Sondre Tesdal Galtung
We show how the sticky dynamics for the one-dimensional pressureless Euler-alignment system can be obtained as an -gradient flow of a convex functional. This is analogous to t…
Equivalence of entropy solutions and gradient flows for pressureless 1D Euler systems
José Antonio Carrillo, Sondre Tesdal Galtung
We study distributional solutions of pressureless Euler systems on the line. In particular we show that Lagrangian solutions, introduced by Brenier, Gangbo, Savaré and Westdickenbe…
Mean field limit for one dimensional opinion dynamics with Coulomb interaction and time dependent weights
Immanuel Ben Porat, José A. Carrillo, Sondre T. Galtung
The mean field limit with time dependent weights for a 1D singular case, given by the attractive Coulomb interactions, is considered. This extends recent results [1,8] for the case…
Shock interactions for the Burgers-Hilbert Equation
Alberto Bressan, Sondre T. Galtung, Katrin Grunert +1
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…
Optimal Shapes for Tree Roots
Alberto Bressan, Sondre T. Galtung, Qing Sun
The paper studies a class of variational problems, modeling optimal shapes for tree roots. Given a measure describing the distribution of root hair cells, we seek to maximize a…
Stumpons are non-conservative traveling waves of the Camassa-Holm equation
Sondre Tesdal Galtung, Katrin Grunert
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 know…
A numerical study of variational discretizations of the Camassa-Holm equation
Sondre Tesdal Galtung, Katrin Grunert
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…
On a Shape Optimization Problem for Tree Branches
Alberto Bressan, Sondre T. Galtung
This paper is concerned with a shape optimization problem, where the functional to be maximized describes the total sunlight collected by a distribution of tree leaves, minus the c…
A semi-discrete scheme derived from variational principles for global conservative solutions of a Camassa-Holm system
Sondre Tesdal Galtung, Xavier Raynaud
We define a kinetic and a potential energy such that the principle of stationary action from Lagrangian mechanics yields a Camassa--Holm system (2CH) as the governing equations. Af…
Competition Models for Plant Stems
Alberto Bressan, Sondre T. Galtung, Audun Reigstad +1
The models introduced in this paper describe a uniform distribution of plant stems competing for sunlight. The shape of each stem, and the density of leaves, are designed in order…
A Convergent Crank-Nicolson Galerkin Scheme for the Benjamin-Ono Equation
Sondre Tesdal Galtung
In this paper we prove the convergence of a Crank-Nicolson type Galerkin finite element scheme for the initial value problem associated to the Benjamin-Ono equation. The proof is b…
Convergence Rates of a Fully Discrete Galerkin Scheme for the Benjamin-Ono Equation
Sondre Tesdal Galtung
We consider a recently proposed fully discrete Galerkin scheme for the Benjamin-Ono equation which has been found to be locally convergent in finite time for initial data in $L^2(\…