W. Jian, S. B. Kuksin, Y. Wu, “Krylov–Bogolyubov averaging”, Uspekhi Mat. Nauk, 2020, Volume 75, Issue 3(453),Pages <nobr>37

This article is cited in 2 papers

Krylov–Bogolyubov averaging

W. Jian^a, S. B. Kuksin^bac, Y. Wu^a

^a School of Mathematical Sciences, Fudan University, Shanghai, China
^b Université Paris VII — Denis Diderot, UFR de Mathématiques, Paris, France
^c St. Petersburg State University

Abstract: A modified approach to the classical Krylov–Bogolyubov averaging method is presented. It was developed recently for studying partial differential equations, enables one to treat Lipschitz perturbations of linear systems with purely imaginary spectrum, and may be generalized to the case of systems of PDEs with small non-linearities.
Bibliography: 10 titles.

Keywords: Krylov–Bogolyubov method, locally Lipschitz vector-field, Hamiltonian equations.

UDC: 517.928.7

MSC: Primary 34C29; Secondary 37J05

Received: 25.04.2019

DOI: 10.4213/rm9933