On Solutions of the One-Dimensional Goldshtik Problem

A one-dimensional analog of the Goldshtik mathematical model for separated flows in an incompressible fluid is considered. The model is a boundary value problem for a second-order ordinary differential equation with discontinuous right-hand side. Some properties of the solutions of the problem, as w...

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Bibliographic Details
Published in:Mathematical Notes 2024-02, Vol.115 (1-2), p.12-20
Main Authors: Baskov, O. V., Potapov, D. K.
Format: Article
Language:English
Subjects:
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639/766/189
639/766/530
639/766/747
Boundary value problems
Differential equations
Flow separation
Fluid flow
Incompressible flow
Incompressible fluids
Mathematical models
Mathematics
Mathematics and Statistics
Vorticity
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Summary:A one-dimensional analog of the Goldshtik mathematical model for separated flows in an incompressible fluid is considered. The model is a boundary value problem for a second-order ordinary differential equation with discontinuous right-hand side. Some properties of the solutions of the problem, as well as the properties of the energy functional for different values of vorticity, are established. An approximate solution of the boundary value problem under study is found using the shooting method.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434624010024