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On a singularly perturbed first-order partial differential equation in the case of intersecting roots of the degenerate equation

  • Partial Differential Equations
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Abstract

For a singularly perturbed first-order partial differential equation, we prove a theorem on the passage to the limit for the case in which the roots of the degenerate equation intersect and the root intersection line meets the initial segment on which the initial condition is posed.

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References

  1. Vasil’eva, A.B. and Butuzov, V.F., Asimptoticheskie metody v teorii singulyarnykh vozmushchenii (Asymptotic Methods in Singular Perturbation Theory), Moscow: Vyssh. Shkola, 1990.

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  2. Butuzov, V.F., Nefedov, N.N., and Shnaider, K.R., Singularly Perturbed Problems in the Case of Stability Change, in Itogi nauki i tekhniki. Sovrem. matematika i ee prilozheniya. Tematicheskie obzory. T. 109. Differents. uravneniya. Singulyarnye vozmushcheniya (Advances in Science and Engineering. Modern Mathematics and Its Applications. Subject Surveys. Vol. 109. Differential Equations. Singular Perturbations), Moscow, 2002.

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  4. Butuzov, V.F., On the Stability and Attraction Domain of a Stationary Nonsmooth Limit Solution of a Singularly Perturbed Parabolic Equation, Zh. Vychisl. Mat. Mat. Fiz., 2006, vol. 46, no. 3, pp. 433–444.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. F. Butuzov & E. A. Derkunova

  2. South-Ural State University, Chelyabinsk, Russia

    V. F. Butuzov & E. A. Derkunova

Authors
  1. V. F. Butuzov
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  2. E. A. Derkunova
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Additional information

Original Russian Text © V.F. Butuzov, E.A. Derkunova, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 2, pp. 180–190.

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Butuzov, V.F., Derkunova, E.A. On a singularly perturbed first-order partial differential equation in the case of intersecting roots of the degenerate equation. Diff Equat 45, 186–196 (2009). https://doi.org/10.1134/S0012266109020050

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  • DOI: https://doi.org/10.1134/S0012266109020050

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