Asymptotics of the Solution of a Bisingular Optimal Boundary Control Problem in a Bounded Domain
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A bisingular problem of optimal boundary control for solutions of an elliptic equation in a bounded domain with a smooth boundary is considered. The coefficient of the Laplacian is assumed to be small, and integral constraints are imposed on the control. A complete asymptotic expansion in powers of the small parameter is obtained for the solution of the problem.
Keywords:singular problems optimal control boundary value problems for systems of partial differential equations asymptotic expansions
This work was supported by the Program of the Presidium of the Russian Academy of Sciences “Fundamental Mathematics and Its Application”: Mathematical methods for motion control in systems with uncertainty and distributed parameters and Hamilton–Jacobi equations.
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