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Real, complex and functional analysis
Regularized asymptotic solutions of integrodifferential equations with a zero operator of differential part and with several quickly varying kernels
M. A. Bobojanova, V. F. Safonov The National Research University "Moscow Power Engineering Institute”,
14, Krasnokazarmennaya str.,
111250, Moscow, Russia
Abstract:
The paper considers an integro-differential equation with the zero operator of the differential part and with several quickly changing integral kernels. The work is a continuation of the authors’ research, carried out earlier for one quickly changing integral kernel. The main ideas of such a generalization and subtleties arising in the development of the algorithm of the Lomov regularization method are fully visible in the case of two quickly changing integral kernels. After constructing an equivalent integro-differential system and its regularization, the theory of normal and unique solvability of the corresponding iterative problems is developed, which is the basis of the algorithm for constructing asymptotic solutions of the original problem.
Keywords:
singularly perturbed, integro-differential equations, regularization of the integral.
Received June 16, 2018, published December 7, 2018
Citation:
M. A. Bobojanova, V. F. Safonov, “Regularized asymptotic solutions of integrodifferential equations with a zero operator of differential part and with several quickly varying kernels”, Sib. Èlektron. Mat. Izv., 15 (2018), 1566–1575
Linking options:
https://www.mathnet.ru/eng/semr1015 https://www.mathnet.ru/eng/semr/v15/p1566
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Abstract page: | 195 | Full-text PDF : | 91 | References: | 25 |
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