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Approximate Solutions to Dirichlet Control Problems for the Wave Equation in Sobolev Classes and Dual Observation Problemsстатья
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Дата последнего поиска статьи во внешних источниках: 21 февраля 2019 г.
- Автор: Potapov M.M.
- Журнал: Computational Mathematics and Mathematical Physics
- Том: 46
- Номер: 12
- Год издания: 2006
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 2092
- Последняя страница: 2109
- DOI: 10.1134/S0965542506120086
- Аннотация: Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces.
- Добавил в систему: Потапов Михаил Михайлович