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

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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
Received: 22 October 2018
Accepted: 29 November 2018
First available in Project Euclid: 15 March 2019

Permanent link to this document
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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