Abstract
We consider a nonlinear singularly perturbed integro-differential system with an integral operator of Fredholm type. We develop and justify an algorithm of the regularization method both in the nonresonance and resonance cases. We show that if the kernel of the integral operator contains a rapidly decaying factor, then the original integro-differential system “is not on the spectrum;” i.e., it is uniquely solvable for any right-hand side (provided that the nonlinear orthogonality conditions are globally solvable). We solve the initialization problem, that is, the problem of describing the original data of the problem for which the convergence holds on the entire time interval considered (including the boundary-layer zone).
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Original Russian Text © A.A. Bobodzhanov, V.F. Safonov, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 2, pp. 251–262.
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Bobodzhanov, A.A., Safonov, V.F. Regularization method for nonlinear integro-differential systems of Fredholm type with rapidly varying kernels. Diff Equat 51, 255–267 (2015). https://doi.org/10.1134/S001226611502010X
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DOI: https://doi.org/10.1134/S001226611502010X