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2014 Optimal Control Problem with Necessary Optimality Conditions for the Viscous Dullin-Gottwald-Holm Equation
Jinsoo Hwang
Abstr. Appl. Anal. 2014: 1-14 (2014). DOI: 10.1155/2014/623129

Abstract

We study the quadratic cost optimal control problems for the viscous Dullin-Gottwald-Holm equation. The main novelty of this paper is to derive the necessary optimality conditions of optimal controls, corresponding to physically meaningful distributive observations. For this we prove the Gâteaux differentiability of nonlinear solution mapping on control variables. Moreover by making use of the second order Gâteaux differentiability of solution mapping on control variables, we prove the local uniqueness of optimal control. This is another novelty of the paper.

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Jinsoo Hwang. "Optimal Control Problem with Necessary Optimality Conditions for the Viscous Dullin-Gottwald-Holm Equation." Abstr. Appl. Anal. 2014 1 - 14, 2014. https://doi.org/10.1155/2014/623129

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022747
MathSciNet: MR3176760
Digital Object Identifier: 10.1155/2014/623129

Rights: Copyright © 2014 Hindawi

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