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Современная математика и ее приложения, 2013, том 89, статья опубликована в англоязычной версии журнала
(Mi cma377)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
An optimal control problem for quasilinear differential equations with Bitsadze–Samarski boundary conditions
D. Devadze, V. Beridze Shota Rustaveli Batumi State University, Batumi, Georgia
Аннотация:
The present paper is devoted to optimal control problems whose behavior is described by quasilinear first-order differential equations on the plane with nonlocal Bitsadze–Samarski boundary conditions. A theorem on the existence and uniqueness of a generalized solution in the space ${C}_{\mu}\left(\overline{G}\right)$ is proved for quasilinear differential equations; necessary optimality conditions are obtained in terms of the maximum principle; the Bitsadze–Samarski boundary-value problem is examined for a first-order linear differential equation; the existence of a solution in the space ${C}_{\mu}^p\left(\overline{G}\right)$ is proved, and an a priori estimate is derived. A necessary and sufficient optimality condition is proved for a linear optimal control problem.
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