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Approximation of the problem of controlling arguments transformation in a nonlinear parabolic equationстатья
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Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.
- Автор: Razgulin A.V.
- Журнал: Computational Mathematics and Mathematical Physics
- Том: 41
- Номер: 12
- Год издания: 2001
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 1752
- Последняя страница: 1764
- Аннотация: The problem of controlling the transformation G(x) of the spatial argument in a nonlinear one-dimensional parabolic functional-differential equation with periodic boundary conditions and a terminal objective functional is studied. For an arbitrary measurable G(x), the existence of generalized solutions to this equation in the space HA1 + γ, 1 (γ ∈ (0, 1/2)) is proved. In the case G(x) ∈ H1(0, 2π), an estimate of the convergence rate to the generalized solution for the equation’s difference-projective approximation scheme in the energy norm of order O(τ^{γ/(1 + γ)} + h^γ) is obtained without a priori assumptions on the smoothness of the solution and without adjustment of the mesh size. For the corresponding approximations of the control problem, an estimate of the convergence rate of the same order with respect to the functional is obtained. Copyright © 2001 by MAIK "Nauka/Interperiodica".
- Добавил в систему: Разгулин Александр Витальевич