Optimal control problem with necessary optimality conditions for the viscous Dullin-Gottwald-Holm equation
type: Item
instance of: scholarly article
title: Optimal control problem with necessary optimality conditions for the viscous Dullin-Gottwald-Holm equation
zbMATH Open document ID: 1474.49042
DOI: 10.1155/2014/623129
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 49K10
Mathematics Subject Classification ID: 49K20
zbMATH DE Number: 7022747
Wikidata QID: Q59040067
author: Jinsoo Hwang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/623129
OpenAlex ID: W2034779140
cites work: An integrable shallow water equation with peaked solitons
cites work: Optimal control of the viscous weakly dispersive Degasperis-Procesi equation
cites work: Q3622496
cites work: Existence and uniqueness of low regularity solutions for the Dullin-Gottwald-Holm equation
cites work: On the well-posedness problem and the scattering problem for the Dullin-Gottwald-Holm equation
cites work: Optimal control of the viscous Dullin-Gottwalld-Holm equation
cites work: Wave Structure and Nonlinear Balances in a Family of Evolutionary PDEs
cites work: Maximum principle for optimal distributed control of the viscous dullin-gottwald-Holm equation
cites work: Q5601627
cites work: Optimal control problems for Kirchhoff type equation with a damping term
cites work: Optimal control problems for the equation of motion of membrane with strong viscosity
cites work: Optimal control problems for an extensible beam equation
cites work: Parameter identification problems for an extensible beam equation
cites work: Optimal control problems governed by some semilinear parabolic equations.
cites work: Q3994914
cites work: Q3684480
cites work: Q3995594
description: scientific article; zbMATH DE number 7022747