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The Cauchy problem for a singularly perturbed integro-differential Fredholm equation

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Abstract

An initial problem is considered for an ordinary singularly perturbed integro-differential equation with a nonlinear integral Fredholm operator. The case when the reduced equation has a smooth solution is investigated, and the solution to the reduced equation with a corner point is analyzed. The asymptotics of the solution to the Cauchy problem is constructed by the method of boundary functions. The asymptotics is validated by the asymptotic method of differential inequalities developed for a new class of problems.

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Authors and Affiliations

  1. Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

    N. N. Nefedov & A. G. Nikitin

Authors
  1. N. N. Nefedov
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  2. A. G. Nikitin
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Original Russian Text © N.N. Nefedov, A.G. Nikitin, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 4, pp. 655–664.

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Nefedov, N.N., Nikitin, A.G. The Cauchy problem for a singularly perturbed integro-differential Fredholm equation. Comput. Math. and Math. Phys. 47, 629–637 (2007). https://doi.org/10.1134/S0965542507040082

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  • DOI: https://doi.org/10.1134/S0965542507040082

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