F. Poupaud, J. Soler. Parabolic limit and stability of the Vlasov-Poisson-FokkerPlanck system. Math. Mod. Meth. in Appl. Sci., 10 (7): 1027-1045, 2000. Home/Search Document Details and Download
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Hydrodynamical Limit For A Drift-Diffusion System Modeling.. - Nieto (2003) (Correct)
....INTRODUCTION The stochastic model governing the dynamics of many particles systems in a surrounding bath is the well known Vlasov Poisson Fokker Planck system. In terms of the thermal velocity and the thermal mean free path, the low field limit of this system was analyzed by Poupaud and Soler in [11], who performed a parabolic limit which preserves the second order di#usive term #t # # div x # # U # ## x # # = 0, t, x) 1.1) x # # , x # # = ## # , t, x) 1.2) # # (0, # 0,# , x , 1.3) where # is a positive (viscosity) constant and # = 1 when we ....
....system (1.4) 1.5) To do that, we consider a sequence of initial conditions # 0,# which converges to # 0 in a suitable space to be precised. We study the associated sequence # # of solutions to (1.1) 1.3) with initial data # 0,# . We shall apply the compactness techniques developed in [8] and [11] in dimension one and in higher dimensions when possible. Then, we shall prove that in the 1 D case the anti symmetry of the Poisson kernel and the global bound of its first derivative allow us to pass to the weak # limit in the space of finite Radon measures uniformly on bounded time intervals. ....
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Poupaud F., Soler J., Parabolic Limit and Stability of the VlasovPoisson -Fokker-Planck System, Math. Mod. Meth. in App. Sci. Vol. 10 No 7 (2000), 1027-1045.
Low And High Field Scaling Limits For The Vlasov- And.. - Arnold, Carrillo.. (1999) (Correct)
....in the squared brackets of (3.7a) and (3.8) resp. n denotes a normal vector on : The electric potential is taken constant in space on each connected component of D , and (x) C(x) Let us nally remark that a rst step in the rigorous proof of this scaling limit has been done recently in [25]. 4 Drift collision balance scaling equations In Section 2 we derived the drift collision balance scaling (DCBS) for the VPFP and WPFP systems. As we did for the low eld scaling, we shall rst consider the equation w t (v r x )w T h 0 [ w (4.1) 1 1 (x) div v (vw (x)r ....
F. Poupaud, J. Soler, Parabolic limit and stability of the Vlasov-PoissonFokker -Planck system, preprint TMR.
Low And High Field Scaling Limits For The Vlasov- And.. - Arnold, Carrillo.. (1999) (Correct)
....of (3.7a) and (3.8) resp. n denotes a normal vector on Omega : The electric potential Phi is taken constant in space on each connected component of Gamma D , and ae(x) C(x) Let us finally remark that a first step in the rigorous proof of this scaling limit has been done recently in [25]. 4 Drift collision balance scaling equations In Section 2 we derived the drift collision balance scaling (DCBS) for the VPFP and WPFP systems. As we did for the low field scaling, we shall first consider the equation j w t (v Delta r x )w Gamma j T h 0 [ Phi]w (4.1) 1 1 (x) div ....
F. Poupaud, J. Soler, Parabolic limit and stability of the Vlasov-PoissonFokker -Planck system, preprint TMR.
Kinetic Models for Chemotaxis and their.. - Chalub, Markowich.. (2003) (Correct)
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F. Poupaud, J. Soler. Parabolic limit and stability of the Vlasov-Poisson-FokkerPlanck system. Math. Mod. Meth. in Appl. Sci., 10 (7): 1027-1045, 2000.
The Langevin or Kramers Approach to Biological Modeling - Hadeler, Hillen, Lutscher (2004) (Correct)
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F. Poupaud and J. Soler, Parabolic limit and stability of the Vlasov-Poisson-FokkerPlanck system, Math. Models Meth. Appl. Sci. 10 (2000) 1027--1045.
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