Exchange of stabilities, symmetry, and nonlinear stability
type: Item
instance of: scholarly article
title: Exchange of stabilities, symmetry, and nonlinear stability
zbMATH Open document ID: 0622.76061
DOI: 10.1007/BF00276872
published in: Archive for Rational Mechanics and Analysis
publication date: 1985-01-01T00:00:00Z
review text: The paper, motivated in large part by the stability in a convection-like problem involving the gravity dependent motion of a suspension of swimming micro-organisms, is aimed to investigate the connection between the symmetric part of a linear operator and stability boundaries determined by the methods of linear theory and of nonlinear energy theory. It is proved that provided exchange of stabilities holds one can correlate linear and nonlinear stability. The method employs an idea of changing the energy norm by an appropriate spatial weight which renders the resulting linear spatial operator symmetric. As the proposed energy stability result relies on finding the maximum of a certain quotient sufficient conditions are given for the demonstration of existence of the maximum.
Mathematics Subject Classification ID: 76E30
Mathematics Subject Classification ID: 76Z99
Mathematics Subject Classification ID: 76E15
zbMATH DE Number: 4010074
zbMATH Keywords: stability
zbMATH Keywords: convection
zbMATH Keywords: gravity dependent motion
zbMATH Keywords: suspension
zbMATH Keywords: swimming micro-organisms
zbMATH Keywords: linear operator
zbMATH Keywords: stability boundaries
zbMATH Keywords: linear theory
zbMATH Keywords: nonlinear energy theory
zbMATH Keywords: nonlinear stability
zbMATH Keywords: energy norm
zbMATH Keywords: energy stability
zbMATH Keywords: existence
author: Giovanni Paolo Galdi
author: Brian Straughan
reviewed by: Andrzej Tylikowski
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4010074