Abstract
We consider an integro-differential system with identically zero operator in the differential part. We construct a regularized asymptotics of the solution of this system for two cases, one in which the integral operator contains an exponentially varying factor and the other in which it does not. On the basis of the resulting asymptotic expansion, we study the passage to the limit in the system and present conditions under which this passage is uniform on the entire range of the independent variable (including the boundary layer region).
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Original Russian Text © M.A. Bobodzhanova, V.F. Safonov, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 4, pp. 519–536.
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Bobodzhanova, M.A., Safonov, V.F. Asymptotic analysis of singularly perturbed integro-differential equations with zero operator in the differential part. Diff Equat 47, 516–533 (2011). https://doi.org/10.1134/S0012266111040070
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DOI: https://doi.org/10.1134/S0012266111040070