Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Secular Terms for the Kinetic Mckean Model

Author(s):

Sergey Anatolievich Dukhnovsky

Moscow State University of Civil Engineering, Department of Applied Mathematics
Yaroslavskoye Shosse 26, 129337 Moscow, Russia
Senior Lecturer
Candidate of Physics and Mathematics Sciences

sergeidukhnvskijj@rambler.ru

Abstract:

In this article, we investigate the kinetic McKean model. The perturbed solution of the Cauchy problem is sought in the form of Fourier series. The Fourier coefficients for the zero and nonzero modes are written out, respectively. The original system is reduced to an infinite system of differential equations. An approximation for the systems is constructed. Under certain assumptions, we find secular terms (non-integrable part). This, in turn, will allow us to prove for the first time the exponential stabilization of the solution in the future.

Keywords

• Fourier series
• kinetic model
• Knudsen parameter
• secular terms

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