Geodesic
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/}
}
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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/