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On the optimal control problem governed by the nonlinear elastic beam equation. (English) Zbl 1153.74030

Summary: We begin with using a dual variational method in proving the existence of solutions to a beam equation with Dirichlet boundary conditions and with a non-monotone nonlinear term. Later we investigate the dependence on a control parameter for the state equation. We find the optimal process for the optimal control problem in which the dynamics is governed by the nonlinear beam equation.

MSC:

74M05 Control, switches and devices (“smart materials”) in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
49J20 Existence theories for optimal control problems involving partial differential equations
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References:

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