Zobrazeno 1 - 10
of 319
pro vyhledávání: '"Karlsen, Kenneth H"'
Autor:
Karlsen, Kenneth H., Pang, Peter H. C.
Convergence of stochastic integrals driven by Wiener processes $W_n$, with $W_n \to W$ almost surely in $C_t$, is crucial in analyzing SPDEs. Our focus is on the convergence of the form $\int_0^T V_n\, \mathrm{d} W_n \to \int_0^T V\, \mathrm{d} W$, w
Externí odkaz:
http://arxiv.org/abs/2404.16157
On the well-posedness of the Cauchy problem for the two-component peakon system in $C^k\cap W^{k,1}$
Autor:
Karlsen, Kenneth H., Rybalko, Yan
This study focuses on the Cauchy problem associated with the two-component peakon system featuring a cubic nonlinearity, constrained to the class $(m,n)\in C^{k}(\mathbb{R}) \cap W^{k,1}(\mathbb{R})$ with $k\in\mathbb{N}\cup\{0\}$.This system extends
Externí odkaz:
http://arxiv.org/abs/2402.04723
This study investigates the $L^1_{\operatorname{loc}}$ compactness of velocity averages of sequences of solutions $\{u_n\}$ for a class of kinetic equations. The equations are examined within both deterministic and stochastic heterogeneous environmen
Externí odkaz:
http://arxiv.org/abs/2311.01234
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 on the deformation of cardiac tissue. The system governs the dynamics
Externí odkaz:
http://arxiv.org/abs/2309.13455
We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required for determin
Externí odkaz:
http://arxiv.org/abs/2309.02208
Autor:
Karlsen, Kenneth H., Towers, John D.
We establish quantitative compactness estimates for finite difference schemes used to solve nonlinear conservation laws. These equations involve a flux function $f(k(x,t),u)$, where the coefficient $k(x,t$ is $BV$-regular and may exhibit discontinuit
Externí odkaz:
http://arxiv.org/abs/2305.18765
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 results in a nonlocal Lagrangian partial differential equation (PDE) mo
Externí odkaz:
http://arxiv.org/abs/2302.03889
Autor:
Karlsen, Kenneth H., Pang, Peter H. C.
The convergence of stochastic integrals driven by a sequence of Wiener processes $W_n\to W$ (with convergence in $C_t$) is crucial in the analysis of stochastic partial differential equations (SPDEs). The convergence we focus on in this paper is of t
Externí odkaz:
http://arxiv.org/abs/2301.06096
Autor:
Karlsen, Kenneth H.
We present a quantitative compensated compactness estimate for stochastic conservation laws, which generalises a previous result of Golse & Perthame (2013) for deterministic equations. With a stochastic modification of Kruzkov's interpolation lemma,
Externí odkaz:
http://arxiv.org/abs/2301.03452
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. We establish the first global-in-time existence result for dissipativ
Externí odkaz:
http://arxiv.org/abs/2211.07046