## International Journal of Differential Equations

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

Jin-soo Hwang

#### 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.

#### Article information

Source
Int. J. Differ. Equ., Volume 2019 (2019), Article ID 3238462, 16 pages.

Dates
Accepted: 29 November 2018
First available in Project Euclid: 15 March 2019

https://projecteuclid.org/euclid.ijde/1552615260

Digital Object Identifier
doi:10.1155/2019/3238462

Mathematical Reviews number (MathSciNet)
MR3914267

#### Citation

Hwang, Jin-soo. Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control Problems. Int. J. Differ. Equ. 2019 (2019), Article ID 3238462, 16 pages. doi:10.1155/2019/3238462. https://projecteuclid.org/euclid.ijde/1552615260

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