Asymptotic of regularized solutions of the ill-posed Cauchy problem for a linear nonautonomous system with delay
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 41-58
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We consider an ill-posed Cauchy problem for a linear nonautonomous system of differential equations with delay. We find asymptotic formulas describing analytical dependances of regularized solutions on the regularization parameter on a finite interval of the negative half-line. The Tikhonov regularization method is used. We chose the stabilizing functional such that it does not generate a compact set in the space of states. The asymptotic formulas are found for smooth enough initial functions which do not provide backward continuation.
Keywords:
differential equations with delay, ill-posed problem, asymptotic methods.
@article{SEMR_2017_14_a83,
author = {P. G. Surkov},
title = {Asymptotic of regularized solutions of the ill-posed {Cauchy} problem for a linear nonautonomous system with delay},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {41--58},
publisher = {mathdoc},
volume = {14},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a83/}
}
TY - JOUR AU - P. G. Surkov TI - Asymptotic of regularized solutions of the ill-posed Cauchy problem for a linear nonautonomous system with delay JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2017 SP - 41 EP - 58 VL - 14 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a83/ LA - ru ID - SEMR_2017_14_a83 ER -
%0 Journal Article %A P. G. Surkov %T Asymptotic of regularized solutions of the ill-posed Cauchy problem for a linear nonautonomous system with delay %J Sibirskie èlektronnye matematičeskie izvestiâ %D 2017 %P 41-58 %V 14 %I mathdoc %U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a83/ %G ru %F SEMR_2017_14_a83
P. G. Surkov. Asymptotic of regularized solutions of the ill-posed Cauchy problem for a linear nonautonomous system with delay. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 41-58. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a83/