Geodesic
Critical travelling waves in one model of the ''reaction-diffusion'' type
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 27 (2021) no. 2, pp. 16-24

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

The paper is devoted to the order reduction for critical traveling wave problems for a reaction-diffusion type systems. The mathematical apparatus is based on the geometric theory of singular perturbations and the canards technique. The use of the method of invariant manifolds of singularly perturbed systems allows us to replace the study of traveling waves of the original PDE system by analyzing their profiles in a ODE system of a lower order.
Mots-clés : singular perturbations, singular perturbations, fast variables
Keywords: slow invariant manifolds, critical travelling waves, integral manifold, order reduction, asymptotic expansion, differential equations, slow variables. 
@article{VSGU_2021_27_2_a1,
     author = {V. A. Sobolev and E. A. Tropkina and E. A. Shchepakina and L. Zhang and J. Wang},
     title = {Critical travelling waves in one model of the ''reaction-diffusion'' type},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {16--24},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2021_27_2_a1/}
}
TY  - JOUR
AU  - V. A. Sobolev
AU  - E. A. Tropkina
AU  - E. A. Shchepakina
AU  - L. Zhang
AU  - J. Wang
TI  - Critical travelling waves in one model of the ''reaction-diffusion'' type
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2021
SP  - 16
EP  - 24
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGU_2021_27_2_a1/
LA  - ru
ID  - VSGU_2021_27_2_a1
ER  - 
%0 Journal Article
%A V. A. Sobolev
%A E. A. Tropkina
%A E. A. Shchepakina
%A L. Zhang
%A J. Wang
%T Critical travelling waves in one model of the ''reaction-diffusion'' type
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2021
%P 16-24
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGU_2021_27_2_a1/
%G ru
%F VSGU_2021_27_2_a1
V. A. Sobolev; E. A. Tropkina; E. A. Shchepakina; L. Zhang; J. Wang. Critical travelling waves in one model of the ''reaction-diffusion'' type. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 27 (2021) no. 2, pp. 16-24. http://geodesic.mathdoc.fr/item/VSGU_2021_27_2_a1/