168 citations · 614 across the 54 of their papers we have counts for
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Global existence of dissipative solutions to the Camassa--Holm equation with transport noise
Luca Galimberti, Helge Holden, Kenneth H. Karlsen +1
We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa--Holm equation perturbed by a convective, position-dependent, noise term.…
Noise-driven bifurcations in a neural field system modelling networks of grid cells
Jose A. Carrillo, Helge Holden, Susanne Solem
The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such…
Uniqueness of conservative solutions for the Hunter-Saxton equation
Katrin Grunert, Helge Holden
We show that the Hunter-Saxton equation and has a unique, global, weak, and conservativ…
Singular Diffusion with Neumann boundary conditions
Giuseppe Maria Coclite, Helge Holden, Nils Henrik Risebro
In this paper we develop an existence theory for the nonlinear initial-boundary value problem with singular diffusion , w…
The Hunter-Saxton equation with noise
Helge Holden, Kenneth H. Karlsen, Peter H. C. Pang
In this paper we develop an existence theory for the Cauchy problem to the stochastic Hunter-Saxton equatio, and prove several properties of the blow-up of its solutions. An import…
A Lipschitz metric for the Camassa--Holm equation
J. A. Carrillo, K. Grunert, H. Holden
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 singular…