Asymptotic Behavior and Stability of a Stationary Boundary-Layer Solution to a Partially Dissipative System of Equations

A boundary value problem for a singularly perturbed partially dissipative system of two ordinary differential equations of the second and first order, respectively, is considered. An asymptotic expansion of its boundary-layer solution in a small parameter is constructed and justified. This solution...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2019-07, Vol.59 (7), p.1148-1171
Main Author: Butuzov, V. F.
Format: Article
Language:English
Subjects:
Asymptotic properties
Asymptotic series
Basins
Boundary value problems
Computational Mathematics and Numerical Analysis
Differential equations
Economic models
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary differential equations
Stability
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Summary:A boundary value problem for a singularly perturbed partially dissipative system of two ordinary differential equations of the second and first order, respectively, is considered. An asymptotic expansion of its boundary-layer solution in a small parameter is constructed and justified. This solution is a stationary solution of the corresponding evolution system of equations with partial derivatives. The asymptotic stability of a stationary boundary-layer solution is proved, and its local basin of attraction is found.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542519070145