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Singularly perturbed partially dissipative systems of equations

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Abstract

We construct an asymptotic expansion in a small parameter of a boundary layer solution of the boundary value problem for a system of two ordinary differential equations, one of which is a second-order equation and the other is a first-order equation with a small parameter at the derivatives in both equations. Such a system arises in chemical kinetics when modeling the stationary process in the case of fast reactions and in the absence of diffusion of one of the reacting substances. A significant feature of the studied problem is that one of the equations of the degenerate system has a triple root. This leads to a qualitative difference in the boundary layer component of the solution compared with the case of simple (single) roots of degenerate equations. The boundary layer becomes multizonal, and the standard algorithm for constructing the boundary layer series turns out to be unsuitable and is replaced with a new algorithm.

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Funding

This research was performed at the Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, and was supported by the Russian Foundation for Basic Research (Grant No. 18-01-00424).

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  1. Physical Faculty, Lomonosov Moscow State University, Moscow, Russia

    V. F. Butuzov

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  1. V. F. Butuzov
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Correspondence to V. F. Butuzov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 210-225 https://doi.org/10.4213/tmf10021.

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Butuzov, V.F. Singularly perturbed partially dissipative systems of equations. Theor Math Phys 207, 579–593 (2021). https://doi.org/10.1134/S0040577921050044

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  • DOI: https://doi.org/10.1134/S0040577921050044

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