Geodesic
Homogenization over the spatial variable in nonlinear parabolic systems
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 80 (2019) no. 1, pp. 63-86

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

We consider boundary value problems for nonlinear parabolic systems whose coefficients are periodic rapidly oscillating functions of the spatial variable. Results on the closeness of time-periodic solutions of an original boundary value problem and the problem homogenized over the spatial variable are presented. The dynamic properties of these equations are studied in near-critical cases of the equilibrium stability problem. Algorithms for constructing the asymptotics of periodic solutions and for calculating the coefficients of the so-called normal forms are developed. In particular, we show that an infinite process of bifurcation and disappearance of a stable cycle can occur with increasing oscillation degree of the coefficients. In addition, we study some classes of problems with a deviation in the spatial variable as well as with a large diffusion coefficient. Logistic delay equations with diffusion and logistic equations with a deviation in the spatial variable, which are important in applications, are studied as examples. The coefficients of these equations are assumed to be rapidly oscillating in the spatial variable. 
@article{MMO_2019_80_1_a1,
     author = {S. A. Kashchenko},
     title = {Homogenization over the spatial variable in nonlinear parabolic systems},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {63--86},
     publisher = {mathdoc},
     volume = {80},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2019_80_1_a1/}
}
TY  - JOUR
AU  - S. A. Kashchenko
TI  - Homogenization over the spatial variable in nonlinear parabolic systems
JO  - Trudy Moskovskogo matematičeskogo obŝestva
PY  - 2019
SP  - 63
EP  - 86
VL  - 80
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MMO_2019_80_1_a1/
LA  - ru
ID  - MMO_2019_80_1_a1
ER  - 
%0 Journal Article
%A S. A. Kashchenko
%T Homogenization over the spatial variable in nonlinear parabolic systems
%J Trudy Moskovskogo matematičeskogo obŝestva
%D 2019
%P 63-86
%V 80
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MMO_2019_80_1_a1/
%G ru
%F MMO_2019_80_1_a1
S. A. Kashchenko. Homogenization over the spatial variable in nonlinear parabolic systems. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 80 (2019) no. 1, pp. 63-86. http://geodesic.mathdoc.fr/item/MMO_2019_80_1_a1/