Approximations of Gol'dshtik's model
D. K. Potapov1
| Annotation | In this paper we consider continuous approximations of the Gol'dshtik problem for separated flows of incompressible fluid. An approximating problem is obtained from the initial problem by small perturbations of a spectral parameter (vorticity) and by the continuous approximations of discontinuous nonlinearity in the phase variable. Using a variational method under certain conditions, we prove the convergence of solutions of the approximating problems to the solutions of the initial problem. A modification for a one-dimensional analogue of the Gol'dshtik mathematical model is considered. The model is a nonlinear differential equation with a boundary condition. Nonlinearity in the equation is continuous and depends on a small parameter. We have a discontinuous nonlinearity, when this parameter tends to zero. The results of the solutions are in accord with the results obtained for the one-dimensional analogue of the Gol'dshtik model. |
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| Keywords | Gol'dshtik model, separated flows, nonlinear differential equation, discontinuous nonlinearity, continuous approximation. |
1Associate Professor of Higher Mathematics Chair, Saint-Petersburg State University, Saint-Petersburg; potapov@apmath.spbu.ru.
Citation: D. K. Potapov, "[Approximations of Gol'dshtik's model]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,13:2 (2011) 100–107 (In Russian)
