Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control Problems

Jin-soo Hwang

International Journal of Differential Equations, 2019, vol. 2019, 1-16

Abstract:

We consider a damped Kirchhoff-type equation with Dirichlet boundary conditions. The objective is to show the Fréchet differentiability of a nonlinear solution map from a bilinear control input to the solution of a Kirchhoff-type equation. We use this result to formulate the minimax optimal control problem. We show the existence of optimal pairs and find their necessary optimality conditions.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:3238462

DOI: 10.1155/2019/3238462

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