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Optimal control problem for a hyperbolic system with mixed control-state constraints involving operator of infinite order. (English) Zbl 1009.49021

The paper considers the problem of minimizing a convex functional over pairs \((y,u)\) from a convex set subject to the state equation \[ y_{tt}(x,t)+ Ay(x,t)= u(x,t),\quad (x,t)\in \mathbb{R}^n\times (0,T), \] and standard initial and boundary conitions. The main feature is that the operator \(A\) is an infinite order selfadjoint elliptic operator. Necessary and sufficient optimality conditions are given.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
49J20 Existence theories for optimal control problems involving partial differential equations
93C20 Control/observation systems governed by partial differential equations
35K20 Initial-boundary value problems for second-order parabolic equations
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