Exponential stability, change of stability and eigenvalue problems for linear time-periodic parabolic equations on \(\mathbb{R}^ N\)
type: Item
instance of: scholarly article
title: Exponential stability, change of stability and eigenvalue problems for linear time-periodic parabolic equations on \(\mathbb{R}^ N\)
zbMATH Open document ID: 0819.35102
author: Daniel Daners
author: Pablo Koch-Medina
published in: Differential and Integral Equations
publication date: 1995-08-24T00:00:00Z
review text: The main aim of the authors is to give necessary and sufficient conditions for the nonnegative weight function \(m(x,t)\) in order that the zero solution of the linear time-periodic equation \(\partial_ t u- \Delta u=- m(x,t)u\), \((x,t)\in \mathbb{R}^ N\times (0,\infty)\) be exponentially stable. The result is applied to the study of the stability properties of the parameter-dependent linear time-periodic equation \(\partial_ t u-\Delta u= \lambda m(x,t)u\), \((x,t)\in \mathbb{R}^ N\times (0,\infty)\), where \(\lambda>0\). They suppose that \(m(x,t)\) belongs to the space of \(\nu\)-Hölder continuous and \(T\)-periodic functions taking values in the space of bounded uniformly continuous functions on \(\mathbb{R}^ N\).
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 597517
zbMATH Keywords: necessary and sufficient conditions
zbMATH Keywords: stability properties
zbMATH Keywords: linear time- periodic equation
reviewed by: Mithat Idemen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 597517