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Regularized asymptotic solutions of singularly perturbed integral equations with a higher-order diagonal degeneration of the kernel and the initialization problem

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Abstract

An algorithm of the regularization method is developed for singularly perturbed integral equations with a higher-order diagonal degeneration of the kernel. The leading term of the asymptotics is analyzed to solve the problem of initialization (that is, extraction of the class of right-hand sides and kernels of the integral operator for which the exact solution of the original equation tends to some limit function as ε → +0 on the entire time interval, including the boundary-layer zone).

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References

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russia

    A. A. Bobodzhanov & V. F. Safonov

Authors
  1. A. A. Bobodzhanov
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  2. V. F. Safonov
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Correspondence to A. A. Bobodzhanov.

Additional information

Original Russian Text © A.A. Bobodzhanov, V.F. Safonov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 2, pp. 221–236.

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Bobodzhanov, A.A., Safonov, V.F. Regularized asymptotic solutions of singularly perturbed integral equations with a higher-order diagonal degeneration of the kernel and the initialization problem. Diff Equat 53, 218–233 (2017). https://doi.org/10.1134/S0012266117020082

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