Asymptotic solution of a singularly perturbed Cauchy problem in the presence of a rational ``simple'' turning point
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Tome 190 (2021), pp. 81-87
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In this paper, based on S. A. Lomov's regularization method, we construct an asymptotic solution of a singularly perturbed Cauchy problem in the case of violation of the stability conditions for the spectrum of the limit operator. In particular, we consider the problem with a “simple” turning point, i.e., where one eigenvalue vanishes for $t=0$ and has the form $t^{m/n}$ (the limit operator is discretely irreversible).
Keywords:
singularly perturbed Cauchy problem, asymptotic solution, regularization method, turning point.
@article{INTO_2021_190_a6,
author = {A. G. Eliseev and T. A. Ratnikova},
title = {Asymptotic solution of a singularly perturbed {Cauchy} problem in the presence of a rational ``simple'' turning point},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {81--87},
publisher = {mathdoc},
volume = {190},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2021_190_a6/}
}
TY - JOUR AU - A. G. Eliseev AU - T. A. Ratnikova TI - Asymptotic solution of a singularly perturbed Cauchy problem in the presence of a rational ``simple'' turning point JO - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory PY - 2021 SP - 81 EP - 87 VL - 190 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/INTO_2021_190_a6/ LA - ru ID - INTO_2021_190_a6 ER -
%0 Journal Article %A A. G. Eliseev %A T. A. Ratnikova %T Asymptotic solution of a singularly perturbed Cauchy problem in the presence of a rational ``simple'' turning point %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2021 %P 81-87 %V 190 %I mathdoc %U http://geodesic.mathdoc.fr/item/INTO_2021_190_a6/ %G ru %F INTO_2021_190_a6
A. G. Eliseev; T. A. Ratnikova. Asymptotic solution of a singularly perturbed Cauchy problem in the presence of a rational ``simple'' turning point. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Tome 190 (2021), pp. 81-87. http://geodesic.mathdoc.fr/item/INTO_2021_190_a6/