Decay rate of the range component of solutions to some semilinear evolution equations
type: Item
instance of: scholarly article
title: Decay rate of the range component of solutions to some semilinear evolution equations
zbMATH Open document ID: 1133.35019
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2007-05-10T00:00:00Z
review text: The author examines the rate of decay to zero, as \(t\to+\infty\), of the projection on the range of \(A\) of the solutions of an equation of the form \(u'+Au+| u| ^{p-1} = 0\) or \(u''+u'+Au+| u| ^{p-1} = 0\) in a bounded domain of \(\mathbb R^N\), where \(A=-\Delta\) with Neumann boundary conditions or \(A=-\Delta-\lambda_1I\) with Dirichlet boundary conditions. In the paper it is shown that this decay is much faster than the decay of the projection on the kernel; it is often exponential, but apparently not always.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 5151300
zbMATH Keywords: range component
zbMATH Keywords: Neumann boundary conditions
author: Alain Haraux
reviewed by: A. A. Martynyuk
MaRDI profile type: Publication
full work available at URL: s00030-006-4019-7
OpenAlex ID: W2018754775
DOI: 10.1007/S00030-006-4019-7
description: scientific article; zbMATH DE number 5151300