Abstract
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.
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References
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V. F. Safonov and A. A. Bobodzhanov, Course in Higher Mathematics. Singularly Perturbed Equations and the Regularization Method (Izd. dom MÉI, Moscow, 2012) [in Russian].
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O. E. Omel’chenko and N. N. Nefedov, “Boundary-layer solutions to quasilinear integro-differential equations of the second order,” Zh. Vychisl. Mat. i Mat. Fiz. 42 (4), 491–503 (2002) [Comput. Math. Math. Phys. 42 (4), 470–482 (2002)].
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Original Russian Text © A. A. Bobodzhanov, V. F. Safonov, 2017, published in Matematicheskie Zametki, 2017, Vol. 102, No. 1, pp. 28–38.
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Bobodzhanov, A.A., Safonov, V.F. Regularized asymptotic solutions of the initial problem for the system of integro-partial differential equations. Math Notes 102, 22–30 (2017). https://doi.org/10.1134/S0001434617070033
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DOI: https://doi.org/10.1134/S0001434617070033