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 Mat. Sb., 2019, Volume 210, Number 11, Pages 76–102 (Mi msb9149)

Asymptotic behaviour of a boundary layer solution to a stationary partly dissipative system with a multiple root of the degenerate equation

V. F. Butuzov

Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We construct asymptotics with respect to a small parameter of a boundary layer solution of the boundary value problem for a system of two ordinary differential equations, one second order and the other first order, with a small parameter multiplying the derivatives in both equations. Systems of this type arise in chemical kinetics as stationary processes in models of fast reactions in the absence of diffusion for one of the reactants. An essential feature of the problem under study is a double root of one of the equations of the degenerate system. This leads to a qualitative change in the boundary layer component of the solution by comparison with the case when all the roots are simple. The boundary layer becomes multizoned, while the standard algorithm for constructing boundary layer series is no longer suitable and has to be replaced by a new one.
Bibliography: 13 titles.

Keywords: singularly perturbed problem with multiple root of the degenerate equation, partly dissipative system, multizone boundary layer.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-01-00424-à This work was carried out with the support of the Russian Foundation for Basic Research (grant no. 18-01-00424-a).

DOI: https://doi.org/10.4213/sm9149

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English version:
Sbornik: Mathematics, 2019, 210:11, 1581–1608

Bibliographic databases:

UDC: 517.928.4

Citation: V. F. Butuzov, “Asymptotic behaviour of a boundary layer solution to a stationary partly dissipative system with a multiple root of the degenerate equation”, Mat. Sb., 210:11 (2019), 76–102; Sb. Math., 210:11 (2019), 1581–1608

Citation in format AMSBIB
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