Floquet exponents and stabilizability in time-periodic parabolic systems
type: Item
instance of: scholarly article
title: Floquet exponents and stabilizability in time-periodic parabolic systems
zbMATH Open document ID: 0722.35043
DOI: 10.1007/BF01447322
author: Guiseppe Da Prato
author: Alessandra Lunardi
published in: Applied Mathematics and Optimization
publication date: 1990-01-01T00:00:00Z
review text: The paper deals with linear \(2\times 2\) parabolic systems of the form \[ U_ t(t)=A(a(t)U(t))+b(t)U(t), \] where A is some second order elliptic operator with suitable boundary conditions and a(\(\cdot)\), b(\(\cdot)\) are T-periodic matrix valued functions such that det(a(\(\cdot))\geq 0\), \(tr(a(\cdot))>0\). The authors give formulae for the accumulation points of the spectra of the evolution operators \(u(\cdot,s)\mapsto u(\cdot,s+T)\). In the case of invertible a(\(\cdot)\), this turns out to be only the origin, while for singular a(\(\cdot)\) there is an additional positive accumulation point. The results apply to questions of stabilizability of solutions of such problems and to the rates of stabilization. Examples include strongly damped wave equations, linear reaction-diffusion systems, and the linearized nerve axon equations.
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35P99
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 4190266
zbMATH Keywords: Floquet exponents
zbMATH Keywords: accumulation points of the spectra
zbMATH Keywords: evolution operators
reviewed by: Hans Engler
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01447322
OpenAlex ID: W2075685928
description: scientific article; zbMATH DE number 4190266