Approximate controllability of the Fitzhugh-Nagumo equation in one dimension
type: Item
instance of: scholarly article
title: Approximate controllability of the Fitzhugh-Nagumo equation in one dimension
zbMATH Open document ID: 1436.93020
author: Shirshendu Chowdhury
author: Mrinmay Biswas
author: Rajib Dutta
published in: Journal of Differential Equations
publication date: 2020-01-22T00:00:00Z
review text: In this interesting paper the authors have discussed the approximate controllability of the FitzHugh-Nagumo (FHN) equation using a localized interior control only for the first equation. The linearized system is not null controllable using a localized interior control since the spectrum of the linearized system has an accumulation point though it is approximately controllable. They showed that the solution of the FHN equation fails to be globally approximately controllable in a given time. But it is possible to move from any steady state to any other steady state arbitrarily close after some appropriate time by a localized interior control, provided that both steady states are in the same connected component of the set of steady states. The authors provided the details of the existence, uniqueness and uniform bound of the solution of the FHN equation. Finally they make some remarks and comments and mention some open questions for the considered system.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93B52
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93D30
zbMATH DE Number: 7155314
zbMATH Keywords: FHN equation
zbMATH Keywords: Rogers-Mcculloch model
zbMATH Keywords: approximate controllability
zbMATH Keywords: Riesz basis
zbMATH Keywords: pole shifting
zbMATH Keywords: Lyapunov functional
reviewed by: Krishnan Balachandran
MaRDI profile type: Publication
full work available at URL: j.jde.2019.10.001
OpenAlex ID: W2981151124
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Wikidata QID: Q127020295
DOI: 10.1016/J.JDE.2019.10.001
description: scientific article