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ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 5, pp. 650–660. c Pleiades Publishing, Inc., 2006. Original Russian Text c P.A. Zakharchenko, E.V. Radkevich, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 5, pp. 610–619. PARTIAL DIFFERENTIAL EQUATIONS On the Properties of the Dispersion Equations of Moment Systems for the Fokker–Planck Equation P. A. Zakharchenko and E. V. Radkevich Moscow State University, Moscow, Russia Received July 9, 2005 DOI: 10.1134/S0012266106050053 1. INTRODUCTION In the present paper, we analyze the asymptotic stability of the Cauchy problem for the system of partial differential equations with constant coefficients [1] ∂M (t, x) ∂M (t, x) (j) I + A + BS M (t, x)=0 (1.1) ∂t ∂x determined by the moment approximation to the Fokker–Planck kinetic equation. Here x =(x ,... ,x ) ∈ R,∂/∂x =(∂/∂x ,... ,∂/∂x ) , 1 n 1 n (1) (n) S ,A ,... ,A are real m×m matrices, I is the identity m×m matrix, and B is a large parameter. There are two fundamentally different approaches to modeling nonequilibrium processes, micro- scopic and phenomenological. The first method for the analysis of nonequilibrium processes uses the description of system states via the distribution function
Differential Equations – Springer Journals
Published: Jun 15, 2006
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