Geodesic
On an error estimate for the averaging method in a~two-frequency problem
Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 29-40

Voir la notice de l'article provenant de la source Math-Net.Ru

The author obtains an unimprovable estimate of the averaging method for a two-frequency problem with analytic right-hand sides under condition $\overline A$, which means a nonzero rate of change of the frequency ratio along trajectories of the averaged system. It turns out to be of order $\varepsilon^{\frac14+\frac1{2(l+1)}}$ for initial data outside a set of measure of order $\varepsilon^{\frac12}$, where $\varepsilon$ is a small parameter of the problem and $l$ is an upper bound for the maximal multiplicity of the roots of a certain finite set of equations (it is assumed that $l>1$). Bibliography: 8 titles. 
@article{SM_1989_62_1_a1,
     author = {V. E. Pronchatov},
     title = {On an error estimate for the averaging method in a~two-frequency problem},
     journal = {Sbornik. Mathematics},
     pages = {29--40},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_62_1_a1/}
}
TY  - JOUR
AU  - V. E. Pronchatov
TI  - On an error estimate for the averaging method in a~two-frequency problem
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 29
EP  - 40
VL  - 62
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1989_62_1_a1/
LA  - en
ID  - SM_1989_62_1_a1
ER  - 
%0 Journal Article
%A V. E. Pronchatov
%T On an error estimate for the averaging method in a~two-frequency problem
%J Sbornik. Mathematics
%D 1989
%P 29-40
%V 62
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1989_62_1_a1/
%G en
%F SM_1989_62_1_a1
V. E. Pronchatov. On an error estimate for the averaging method in a~two-frequency problem. Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 29-40. http://geodesic.mathdoc.fr/item/SM_1989_62_1_a1/