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Asymptotic Analysis of Abstract Linear Kinetic Equations
Author(s) -
Banasiak J.
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199604)19:6<481::aid-mma778>3.0.co;2-d
Subject(s) - mathematics , moment (physics) , operator (biology) , zeroth law of thermodynamics , kinetic theory , fokker–planck equation , diffusion equation , mathematical analysis , diffusion , kinetic energy , order (exchange) , collision , asymptotic analysis , classical mechanics , partial differential equation , physics , theoretical physics , quantum mechanics , biochemistry , chemistry , economy , computer security , finance , repressor , computer science , transcription factor , economics , gene , service (business)
In this paper we provide a theory of the asymptotic expansion for an abstract kinetic equation. We show that the modified Chapman–Enskog procedure, introduced in [19], gives the error of order of ε 2 , uniformly in time, on the second level of approximation and in particular that the zeroth moment of the solution (the spatial density of particles) can be approximated by the solution of the diffusion‐type equation with the same accuracy. The theory is applied to several types of kinetic equations with the Fokker–Planck collision operator.