Abstract
We construct and justify the asymptotics of the solution of a boundary value problem for a singularly perturbed system of two second-order ordinary differential equations that contain distinct powers of a small parameter multiplying second-order derivatives for the case of a multiple root of the degenerate equation. The root multiplicity results in changes in the structure of the asymptotics of the boundary layer solution as compared with the case of a simple root, in particular, in changes in the scale of the boundary layer variables.
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Butuzov, V.F., On Specific Features of a Boundary Layer in Singularly Perturbed Problems with a Multiple Root of the Degenerate Equation, Mat. Zametki, 2013, vol. 94, no. 1, pp. 68–80.
Vasil’eva, A.B. and Butuzov, V.F., Asimptoticheskie metody v teorii singulyarnykh vozmushchenii (Asymptotic Methods in Singular Perturbation Theory), Moscow: Vyssh. Shkola, 1990.
Pao, C.V., Nonlinear Parabolic and Elliptic Equations, New York, 1992.
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Original Russian Text © V.F. Butuzov, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 2, pp. 175–186.
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Butuzov, V.F. Asymptotics of the solution of a system of singularly perturbed equations in the case of a multiple root of the degenerate equation. Diff Equat 50, 177–188 (2014). https://doi.org/10.1134/S0012266114020050
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DOI: https://doi.org/10.1134/S0012266114020050