Fréchet differentiability for a damped sine-Gordon equation
type: Item
instance of: scholarly article
title: Fréchet differentiability for a damped sine-Gordon equation
zbMATH Open document ID: 1185.35323
author: Semion Gutman
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-11-06T00:00:00Z
review text: An initial boundary value problem for the damped sine-Gordon equation with a variable diffusion coefficient is considered. The aim is to identify coefficients in equation such that the solution attains a desired behavior. This leads to an optimal control problem for which the necessary condition of optimality is written in form of a variational inequality. Much effort is done to prove the Gâteaux differentiability of the solution map and the Fréchet differentiability of the objective functional.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35Q93
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 5626927
zbMATH Keywords: optimal control
zbMATH Keywords: parameter identification
zbMATH Keywords: Fréchet differentiability
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.06.074
OpenAlex ID: W2088510318
cites work: Q4040192
cites work: Influence of solitons in the initial state on chaos in the driven damped sine-Gordon system
cites work: Q4399897
cites work: Identification of Discontinuous Parameters in Flow Equations
cites work: OPTIMAL PARAMETERS FOR A DAMPED SINE-GORDON EQUATION
cites work: Optimal Control Problems for Nonlinear Hyperbolic Distributed Parameter Systems with Damping Terms
cites work: IDENTIFICATION PROBLEMS OF DAMPED SINE-GORDON EQUATIONS WITH CONSTANT PARAMETERS
cites work: Fréchet differentiability of solution mappings for semilinear second order evolution equations
cites work: Q4724101
cites work: Q5601627
cites work: Q5634306
cites work: Infinite-dimensional dynamical systems in mechanics and physics.
DOI: 10.1016/J.JMAA.2009.06.074
description: scientific article; zbMATH DE number 5626927