152 citations · 152 across the 9 of their papers we have counts for
10 papers
Existence of strong initial traces for stochastic conservation laws
Marko Erceg, Nikola Konatar, Kenneth Karlsen +1
We prove existence and uniqueness of a strong initial trace for every bounded kinetic solution of a stochastic scalar conservation law, although no initial value is prescribed and…
Structure-preserving LDG methods for linear and nonlinear transport equations with gradient noise
Thomas Christiansen, Kenneth H. Karlsen
We develop local discontinuous Galerkin (LDG) methods for conservation laws with heterogeneous stochastic fluxes, where the Stratonovich-driven transport terms may be linear or non…
Stochastic Euler Equations with Pseudo-differential Noise: Continuous and Discontinuous Perturbations in Compressible and Incompressible Flows
Kenneth. H. Karlsen, Hao Tang, Feng-Yu Wang
We study stochastic Euler equations in compressible and incompressible regimes, on the whole space and the torus, driven by mixed multiplicative noise: continuous Stratonovich/Itô…
Regularity of velocity averages in kinetic equations with heterogeneity
Marko Erceg, Kenneth H. Karlsen, Darko Mitrović
This study investigates the regularity of kinetic equations with spatial heterogeneity. Recent progress has shown that velocity averages of weak solutions in () are…
Semi-discrete heat equations with variable coefficients and the parametrix method
Ulrik S. Fjordholm, Kenneth H. Karlsen, Peter H. C. Pang
We develop a parametrix approach for constructing solutions and establishing grid-size independent estimates for semi-discrete heat equations with variable coefficients. While the…
On the regularity of entropy solutions to stochastic degenerate parabolic equations
Marko Erceg, Kenneth H. Karlsen, Darko Mitrović
We study the regularity of entropy solutions for quasilinear parabolic equations with anisotropic degeneracy and stochastic forcing. Building on previous works, we establish space-…
Upwind filtering of scalar conservation laws
Giuseppe Maria Coclite, Kenneth Hvistendahl Karlsen, Nils Henrik Risebro
We study a class of multi-dimensional non-local conservation laws of the form , where the standard local divergence $\operatornam…
Convergence of stochastic integrals with applications to transport equations and conservation laws with noise
Kenneth H. Karlsen, Peter H. C. Pang
Convergence of stochastic integrals driven by Wiener processes , with almost surely in , is crucial in analyzing SPDEs. Our focus is on the convergence of the…
Velocity averaging under minimal conditions for deterministic and stochastic kinetic equations with irregular drift
Marko Erceg, Kenneth H. Karlsen, Darko Mitrović
This study investigates the compactness of velocity averages of sequences of solutions for a class of kinetic equations. The equations are exam…
A theory of -dissipative solvers for scalar conservation laws with discontinuous flux
Boris Andreianov, Kenneth H. Karlsen, Nils Henrik Risebro
We propose a general framework for the study of contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of precedin…