Geodesic
Asymptotic solutions of integro-differential equations with partial derivatives and with rapidly varying kernel
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1623-1632

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In the paper, ideas of the Lomov regularization method are generalized to the Cauchy problem for a singularly perturbed partial integro-differential equation in the case when the integral term contains a rapidly varying kernel. Regularization of the problem is carried out, the normal and unique solvability of general iterative problems is proved.
Keywords: singularly perturbed, partial integro differential equation, regularization of an integral, solvability of iterative problems. 
@article{SEMR_2019_16_a103,
     author = {B. T. Kalimbetov and N. A. Pardaeva and L. D. Sharipova},
     title = {Asymptotic solutions of integro-differential equations with partial derivatives and with rapidly varying kernel},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1623--1632},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a103/}
}
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B. T. Kalimbetov; N. A. Pardaeva; L. D. Sharipova. Asymptotic solutions of integro-differential equations with partial derivatives and with rapidly varying kernel. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1623-1632. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a103/