ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 34, 35 Ilolov, Mamadsho, Tajik State National University, Dushanbe, Tajikistan Invariant tori of evolution equations In this work, existence, uniqueness and smoothness of the invariant tori are considered for a class of evolution equations

\frac{dφ}{dt} = a(φ), \frac{dx}{dt} = Ax(φ) + g(φ, x)(g(0, x) = 0)

with smooth function a : T^{m} → IR^{n}, closed linear operator A : D(A) ⊂ X → X and g ∈ C^{k}(T^{m}, X) for some k ≥ 1, where T^{m} − m–dimensional tori, IR^{n} − n–dimensional space, X− Banach space. Applications to some types of partial differential equations are presented. The results have been partly obtained in joint work with A. M. Samoilenko.