The regularized asymptotics of a~solution of the Cauchy problem in the presence of a~weak turning point of the limit operator
Sbornik. Mathematics, Tome 212 (2021) no. 10, pp. 1415-1435
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An asymptotic solution of the linear Cauchy problem in the presence of a ‘weak’ turning point of the limit operator is built using Lomov's regularization method. The major singularities of the problem are written out in an explicit form. Estimates are given with respect to $\varepsilon$, which characterise the behaviour of the singularities as $\varepsilon\to 0$. The asymptotic convergence of the regularized series is proved. The results of the work are illustrated by an example.
Bibliography: 8 titles.
Keywords:
singular Cauchy problem, asymptotic series, regularization method, turning point.
@article{SM_2021_212_10_a2,
author = {A. G. Eliseev},
title = {The regularized asymptotics of a~solution of the {Cauchy} problem in the presence of a~weak turning point of the limit operator},
journal = {Sbornik. Mathematics},
pages = {1415--1435},
publisher = {mathdoc},
volume = {212},
number = {10},
year = {2021},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2021_212_10_a2/}
}
TY - JOUR AU - A. G. Eliseev TI - The regularized asymptotics of a~solution of the Cauchy problem in the presence of a~weak turning point of the limit operator JO - Sbornik. Mathematics PY - 2021 SP - 1415 EP - 1435 VL - 212 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_2021_212_10_a2/ LA - en ID - SM_2021_212_10_a2 ER -
%0 Journal Article %A A. G. Eliseev %T The regularized asymptotics of a~solution of the Cauchy problem in the presence of a~weak turning point of the limit operator %J Sbornik. Mathematics %D 2021 %P 1415-1435 %V 212 %N 10 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2021_212_10_a2/ %G en %F SM_2021_212_10_a2
A. G. Eliseev. The regularized asymptotics of a~solution of the Cauchy problem in the presence of a~weak turning point of the limit operator. Sbornik. Mathematics, Tome 212 (2021) no. 10, pp. 1415-1435. http://geodesic.mathdoc.fr/item/SM_2021_212_10_a2/