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The problem of oscillations of a two-sided segment in a stratified fluidстатья
Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.
- Авторы: Korpusov M.O., Pletner Yu D., Sveshnikov A.G.
- Журнал: Computational Mathematics and Mathematical Physics
- Том: 37
- Номер: 8
- Год издания: 1997
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 936
- Последняя страница: 942
- Аннотация: An initial-boundary value problem for the equation (uxx+uyy−u)tt+uxx=0 is considered in R2∖Γ, where Γ is a simple C1,λ-arc (λ>0) of finite length. Time-dependent Dirichlet data are given on both sides of Γ; the initial conditions are homogeneous and the natural behaviour is required at infinity and near the end-points of Γ. The problem describes waves arising from the rest state due to a given pressure distribution on each side of Γ placed in an exponentially stratified, inviscid incompressible fluid; u is related to the velocity potential. Techniques based on the so-called angular potentials [S. A. Gabov and A. G. Sveshnikov, Linear problems in the theory of unsteady internal waves (Russian), "Nauka'', Moscow, 1990; MR1109492 (92i:76015)] are applied for reducing the problem to a system of two integral equations. One of them has an explicit solution, and the other is shown to be solvable. Thus, the problem has a classical solution, which is shown to be unique. {See also the following review [MR1480655 (98m:76044)].}
- Добавил в систему: Корпусов Максим Олегович