Geodesic
Asymptotics of regularized solutions of an ill-posed Cauchy problem for an autonomous linear system of differential equations with commensurable delays
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 4, pp. 107-118
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For an autonomous linear system of differential equations with commensurable delays, asymptotic formulas are found that describe the analytic dependences of regularized solutions of the system on the regularization parameter. The problem is solved under the requirement that the initial function is sufficiently smooth but with the violation of the conditions that guarantee the continuous extension of solution in the direction of decreasing time.
Keywords: differential equations with delay, ill-posed problem, asymptotic methods. 
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Yu. F. Dolgii; P. G. Surkov. Asymptotics of regularized solutions of an ill-posed Cauchy problem for an autonomous linear system of differential equations with commensurable delays. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 4, pp. 107-118. http://geodesic.mathdoc.fr/item/TIMM_2013_19_4_a10/

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