107 citations · 250 across the 39 of their papers we have counts for
46 papers
A duality approach to the fractional Laplacian with measure data
Kenneth H. Karlsen, Francesco Petitta, Suleyman Ulusoy
We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like with vanishing condition…
Stochastic electromechanical bidomain model
Mostafa Bendahmane, Kenneth H. Karlsen, Fatima Mroue
We analyze a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect…
Convergent finite difference schemes for stochastic transport equations
Ulrik S. Fjordholm, Kenneth H. Karlsen, Peter H. C. Pang
We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish stability and convergence of the difference approximations…
Compactness estimates for difference schemes for conservation laws with discontinuous flux
Kenneth H. Karlsen, John D. Towers
We establish quantitative compactness estimates for finite difference schemes used to solve nonlinear conservation laws. These equations involve a flux function , wher…
A nonlocal Lagrangian traffic flow model and the zero-filter limit
Giuseppe M. Coclite, Kenneth H. Karlsen, Nils Henrik Risebro
In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This r…
Quantitative compactness estimates for stochastic conservation laws
Kenneth H. Karlsen
We present a quantitative compensated compactness estimate for stochastic conservation laws, which generalises a previous result of Golse & Perthame (2013) for deterministic equati…