Geodesic
Initialization problem for singularly perturbed integro-differential and integral Volterra equations of the second kind
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Tome 191 (2021), pp. 38-46.

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The initialization problem for singularly perturbed integro-differential and integral systems of Volterra equations of the second kind is solved by the Lomov regularization method.
Mots-clés : singular perturbation
Keywords: initialization problem, regularization method, Volterra integro-differential equation. 
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A. G. Eliseev; T. A. Ratnikova; D. A. Shaposhnikova. Initialization problem for singularly perturbed integro-differential and integral Volterra equations of the second kind. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Tome 191 (2021), pp. 38-46. http://geodesic.mathdoc.fr/item/INTO_2021_191_a4/

[1] Filatov A. N., Shershikov V. V., Asimptoticheskie metody v atmosfernykh modelyakh, Gidrometeoizdat, L., 1988

[2] Lomov S. A., Vvedenie v obschuyu teoriyu singulyarnykh vozmuschenii, Nauka, M., 1981

[3] Eliseev A. G., Shaposhnikova D. A., “Zadacha initsializatsii singulyarno vozmuschennogo integralnogo uravneniya Volterra vtorogo roda s diagonalnym vyrozhdeniem v sluchae $n\ge 3$”, Vestn. MEI., 3 (2015), 143–144

[4] Ipatova V. M., “Zadachi initsializatsii dlya modelei obschei tsirkulyatsii atmosfery”, Tr. MFTI., 4:2 (2012), 121–130 | MR