168 citations · 614 across the 54 of their papers we have counts for
61 papers
Well-posedness and error estimates for coupled systems of nonlocal conservation laws
Aekta Aggarwal, Helge Holden, Ganesh Vaidya
This article deals with the error estimates for numerical approximations of the entropy solutions of coupled systems of nonlocal hyperbolic conservation laws. The systems can be st…
On the accuracy of the finite volume approximations to nonlocal conservation laws
Aekta Aggarwal, Helge Holden, Ganesh Vaidya
In this article, we discuss the error analysis for a certain class of monotone finite volume schemes approximating nonlocal scalar conservation laws, modeling traffic flow and crow…
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…
Strong solutions of a stochastic differential equation with irregular random drift
Helge Holden, Kenneth H. Karlsen, Peter H. C. Pang
We present a well-posedness result for strong solutions of one-dimensional stochastic differential equations (SDEs) of the form $$\mathrm{d} X= u(ω,t,X)\, \mathrm{d} t + \frac12 σ(…