Geodesic
Regularization of an ill-posed Cauchy problem for an autonomous system with delay with the use of a~class of stabilizers
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 3, pp. 234-245

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For an autonomous linear system of differential equations with delay, we find asymptotic formulas for the analytic dependence of regularized solutions of this system on a regularization parameter on a finite closed interval of the negative semiaxis. We use the Tychonoff regularization method with a stabilizing functional not generating a compact set in the state space. The problem is solved for sufficiently smooth initial functions, which, however, do not satisfy the conditions that guarantee a continuous extension of solutions to decreasing time.
Keywords: differential equations with delay, ill-posed problem, asymptotic methods. 
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     author = {P. G. Surkov},
     title = {Regularization of an ill-posed {Cauchy} problem for an autonomous system with delay with the use of a~class of stabilizers},
     journal = {Trudy Instituta matematiki i mehaniki},
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P. G. Surkov. Regularization of an ill-posed Cauchy problem for an autonomous system with delay with the use of a~class of stabilizers. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 3, pp. 234-245. http://geodesic.mathdoc.fr/item/TIMM_2014_20_3_a15/