Butuzov, V. F. Asymptotic behaviour of a boundary layer solution to a stationary partly dissipative system with a multiple root of the degenerate equation. (English. Russian original) Zbl 1480.34077 Sb. Math. 210, No. 11, 1581-1608 (2019); translation from Mat. Sb. 210, No. 11, 76-102 (2019). Summary: 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. Cited in 4 Documents MSC: 34E13 Multiple scale methods for ordinary differential equations 35K57 Reaction-diffusion equations 34B60 Applications of boundary value problems involving ordinary differential equations Keywords:singularly perturbed problem with multiple root of degenerate equation; partly dissipative system; multizone boundary layer PDFBibTeX XMLCite \textit{V. F. Butuzov}, Sb. Math. 210, No. 11, 1581--1608 (2019; Zbl 1480.34077); translation from Mat. Sb. 210, No. 11, 76--102 (2019) Full Text: DOI References: [1] S. L. Hollis and J. J. Morgan 1992 Partly dissipative reaction-diffusion systems and a model of phosphorus diffusion in silicon Nonlinear Anal.19 5 427-440 · Zbl 0773.35029 [2] A. B. Vasil’eva and V. F. 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