Geodesic
Regularized Asymptotic Solutions of the Initial Problem for the System of Integro-Partial Differential Equations
Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 28-38.

Voir la notice de l'article provenant de la source Math-Net.Ru

The Lomov regularization method [1] is generalized to integro-partial differential equations. It turns out that the regularization procedure essentially depends on the type of integral operator. The case in which the upper limit of the integral is not the differentiation variable is the most difficult one. It is not considered in the present paper. Only the case in which the upper limit of the integral operator coincides with the differentiation variable is studied. For such problems, an algorithm for constructing regularized asymptotics is developed.
Keywords: singularly perturbed equation, integro-partial differential equation, regularization of an integral. 
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A. A. Bobodzhanov; V. F. Safonov. Regularized Asymptotic Solutions of the Initial Problem for the System of Integro-Partial Differential Equations. Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 28-38. http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a3/

[1] S. A. Lomov, Vvedenie v obschuyu teoriyu singulyarnykh vozmuschenii, Nauka, M., 1981 | MR | Zbl

[2] V. F. Safonov, A. A. Bobodzhanov, Kurs vysshei matematiki. Singulyarno vozmuschennye uravneniya i metod regulyarizatsii, Izd. dom MEI, M., 2012

[3] S. A. Lomov, I. S. Lomov, Osnovy matematicheskoi teorii pogranichnogo sloya, Izd-vo Mosk. un-ta, M., 2011

[4] O. E. Omelchenko, N. N. Nefedov, “Pogransloinye resheniya v kvazilineinykh integrodifferentsialnykh uravneniyakh vtorogo poryadka”, Zh. vychisl. matem. i matem. fiz., 42:4 (2002), 491–503 | MR | Zbl