Vlasov and McKean-Vlasov PDEs.
NUMERICAL METHOD FOR FBSDES OF MCKEAN-VLASOV TYPE
... µq and taken at the continuous coordinate ...These PDEs arise in the study of large population stochastic control problems, either of mean field game type, see for instance [12, 13, 20, 30] or [18, ...12] ...
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Global solvability of a networked integrate-and-fire model of McKean-Vlasov type
... probability and PDEs, the deep core of the strategy being ...1 and the density of the initial condition decays linearly at the threshold, it is proven that the system induces a natural contraction in ...
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Analytical approximations of non-linear SDEs of McKean-Vlasov type
... In order to achieve higher orders expansions for the marginal density P t = ˜ P t ε | ε=1 , we follow the strategy explained previously. Hereafter throughout this subsection we fix N ∈ N ∗ and we assume the ...
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Diffusive processes on the Wasserstein space : coalescing models, regularization properties and McKean-Vlasov equations
... line, which is the space of probability measures with a finite second-order moment endowed with the L 2 -Wasserstein distance. There are many reasons for explaining our main interest in the L 2 - Wasserstein distance: ...
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Control of McKean-Vlasov systems and applications
... controlled McKean-Vlasov ...DP, and shall rely on a special Itô’s chain rule for flows of probability measures as recently developed in [ BLPR17 ] and [ CCD15 ], and used in [ CD14 ] ...
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Lagrangian/Eulerian solvers and simulations for Vlasov-Poisson
... Résumé. Au moyen d'une méthode de réduction décrite dans [10, 14, 22] nous construisons une approx- imation hyperbolique de l'équation de Vlasov dans laquelle la dépendance en vitesse est supprimée. La réduction ...
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Invariant measures of the 2D Euler and Vlasov equations
... uniform and depends strongly on the boundary ...27] and references therein for recent developments of the kinetic theory of ...long and very interesting history, with wonderful pieces of mathematical ...
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From Vlasov–Poisson and Vlasov–Poisson–Fokker–Planck Systems to Incompressible Euler Equations: the case with finite charge
... the Vlasov–Poisson system to the Incompressible Euler ...the Vlasov–Poisson–Fokker– Planck system which induces dissipative ...non–homogeneous and where the Euler equation is replaced by the Lake ...
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The Vlasov-Ampère system and the Bernstein-Landau paradox *
... the Vlasov-Poisson system we study the Vlasov-Amp` ere ...the Vlasov-Amp` ere system as a Schr¨ odinger equation where the Vlasov-Amp` ere operator plays the role of the ...the ...
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Etude numérique des solutions périodiques du système de Vlasov-Maxwell
... Introduction 0.1 Présentation générale des travaux Ce travail a consisté essentiellement en une étude théorique des solutions périodiques des systèmes de Vlasov-Poisson et Vlasov-Maxwell[r] ...
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A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: The one-dimensional case
... existence and uniqueness of the local solution to the non-linear martingale problem solved by any limit of the Picard procedure, and to suitably paste local solutions when constructing the global ...
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Finite Volume Schemes for Vlasov
... example, and this relation remains true from the stability of the LAG-2d + 1 scheme, for all d ∈ ...odd and even order interpolation ...smooth and upwind approximation of one degree less is used ...
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SYMETRIZATION OF VLASOV-POISSON EQUATIONS
... linearized Vlasov-Amp`ere equation around ...linear Vlasov-Poisson equation (1.9) and detail the sensibility of the asymptotic damping with respect to the Debye ...linear Vlasov-Amp`ere ...
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Trapping scaling for bifurcations in Vlasov systems
... pansion and emphasize the main physical points (Section II A), then present a more detailed computation (Section II ...computations, and provide precise predictions, as well as push the computations at ...
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A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: The two-dimensional case
... 1 and χ > 0) in the framework of [ 6 ], we see that we have removed the assumption on the smallness of the initial datum ...emerges) and, then, such solution is globalized (where C2 ...
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Effet de dérive sur les oscillations forcées d'un plasma de Vlasov
... Une direction de départ de cette recherche est l'étude des oscillations électrostatiques longitudinales d'un plasma en dérive, étude devant permettre d'effectuer par[r] ...
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Noise prevents collapse of Vlasov--Poisson point charges
... is obtained under general conditions on the covariance matrix Q: specific examples are given in Section 3. The remainder of the paper is devoted to the proof of Theorem 1. We first discuss the structure of the noise ...
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Algebraic damping in the one-dimensional Vlasov equation
... A Vlasov equation usually admits a continuous infinity of stationary ...space, and addressed the issue of the asymptotic behavior of a small perturbation through a Laplace transform analysis of the ...
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Unstable manifold expansion for Vlasov-Fokker-Planck equation
... In the standard situation where only one, or two, eigenvalues cross the imaginary axis at the bifurcation point, while the others keep a finite, negative, real part, the coefficients c3, c5, . . . do not diverge. In this ...
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An Eulerian Vlasov code for plasma-wall interactions
... power and accessibility of computing resources, the accurate numerical simulation of plasma-wall interactions remains a challenging ...time and space scales, dynamical regimes (from collisional to ...
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