Controls insensitizing the norm of the solution of a semilinear heat equation
type: Item
instance of: scholarly article
title: Controls insensitizing the norm of the solution of a semilinear heat equation
zbMATH Open document ID: 0852.35070
author: O. Bodart
author: Caroline Fabre
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-12-09T00:00:00Z
review text: The authors consider a semilinear heat equation with partially known initial and boundary conditions. It is shown that the so-called insensitivity conditions are equivalent to a particular nonlinear exact controllability problem for parabolic equations. Solving the linear problem leads to the proof of a non-trivial uniqueness property which is also used to characterize a particular subset of the admissible controls. This characterization is made thanks to a convex duality theorem and allows the authors to use a fixed-point theorem and get the result for the nonlinear case.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 861790
zbMATH Keywords: semilinear heat equation
zbMATH Keywords: controllability
reviewed by: Georgiĭ Anatol'evich Sviridyuk
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1382
OpenAlex ID: W2089868271
DOI: 10.1006/JMAA.1995.1382
description: scientific article; zbMATH DE number 861790