Geodesic
On the Cauchy problem for the descriptor equation with perturbation in the right-hand side
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 51-56

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

We consider the Cauchy problem for a differential equation with a Fredholm operator acting on the derivative whose right-hand side depends on a small parameter. We examine the behavior of solutions as the parameter tends to zero and establish a connection between the sensitivity of solutions to perturbations and the relation between the lengths of some Jordan chains and the orders of the poles of some operators. The conditions for the appearance of boundary layers are determined.
Keywords: descriptor equation, boundary layer, Newton diagram.
Mots-clés : perturbation 
@article{INTO_2021_195_a5,
     author = {S. P. Zubova and E. V. Raetskaya},
     title = {On the {Cauchy} problem for the descriptor equation with perturbation in the right-hand side},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {51--56},
     publisher = {mathdoc},
     volume = {195},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_195_a5/}
}
TY  - JOUR
AU  - S. P. Zubova
AU  - E. V. Raetskaya
TI  - On the Cauchy problem for the descriptor equation with perturbation in the right-hand side
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 51
EP  - 56
VL  - 195
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_195_a5/
LA  - ru
ID  - INTO_2021_195_a5
ER  - 
%0 Journal Article
%A S. P. Zubova
%A E. V. Raetskaya
%T On the Cauchy problem for the descriptor equation with perturbation in the right-hand side
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 51-56
%V 195
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2021_195_a5/
%G ru
%F INTO_2021_195_a5
S. P. Zubova; E. V. Raetskaya. On the Cauchy problem for the descriptor equation with perturbation in the right-hand side. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 51-56. http://geodesic.mathdoc.fr/item/INTO_2021_195_a5/