AVERAGING OF DIFFERENTIAL-INCLUSIONS WITH FAST AND SLOW VARIABLESстатья
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Дата последнего поиска статьи во внешних источниках: 7 декабря 2013 г.
Аннотация:It is shown that for any solution (x(·),y(·)) to the system of differential inclusions
x ' (t)∈μF(t,x(t),y(t),μ),y ' (t)∈G(t,x(t),y(t),μ),x(t 0 )=x 0 ,y(t 0 )=y 0 ,
where μ∈(t 0 ,μ 0 ) and μ 0 depends on ϵ, there exists a solution ξ (·) to the average differential inclusion ξ ' (t)∈μF 0 (ξ),ξ(t 0 )=x 0 , such that |x(t)-ξ(t)|<ϵ for t∈[t 0 ,t 0 +μ -1 ]. Except of some regularity of F, G, F 0 it is assumed that for every ϵ>0 there exists s ϵ >0 such that for every s>s ϵ and every solution y ¯(·) to the generating inclusion y ¯ ' (t)∈G(t,x 0 ,y ¯(t),0),y ¯(t 0 )=y 0 we have
1 s∫ t 0 t 0 +s F(t,x 0 ,y ¯(t),0)dt⊂F 0 ϵ (x 0 )·
Some methods for the construction of an averaged inclusion are described.