H. Holden

activity

19932023

most citedThe Kolmogorov-Riesz compactness theorem

168 citations · 614 across the 54 of their papers we have counts for

collaborators

Showing 2009Show all

5 papers · 1 filter

math.AP2009

Global semigroup of conservative solutions of the nonlinear variational wave equation

Helge Holden, Xavier Raynaud

We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation $u_{tt} - c (u) (c (u) u_{x})_{x} = 0$ . We allow for initial data $u ∣_{t = 0}$ …

math.AP2009

Operator splitting for the KdV equation

Helge Holden, Kenneth H. Karlsen, Nils Henrik Risebro +1

We provide a new analytical approach to operator splitting for equations of the type $u_{t} = A u + B (u)$ where $A$ is a linear operator and $B$ is quadratic. A particular example is the…

math.CA2009★ 168 cited

The Kolmogorov-Riesz compactness theorem

Harald Hanche-Olsen, Helge Holden

We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem…

math.AP2009★ 1 cited

Lipschitz metric for the Hunter-Saxton equation

Alberto Bressan, Helge Holden, Xavier Raynaud

We study stability of solutions of the Cauchy problem for the Hunter-Saxton equation $u_{t} + u u_{x} = \frac{1}{4} (\int_{- \infty}^{x} u_{x}^{2} d x - \int_{x}^{\infty} u_{x}^{2} d x)$ with initial data $u_{0}$ .…

math.AP2009

Symmetric waves are traveling waves

Mats Ehrnström, Helge Holden, Xavier Raynaud

We show that horizontally symmetric water waves are traveling waves. The result is valid for the Euler equations, and is based on a general principle that applies to a large class…