Resolvent estimates and quantification of nonlinear stability
type: Item
instance of: scholarly article
title: Resolvent estimates and quantification of nonlinear stability
zbMATH Open document ID: 0962.35021
author: Heinz-Otto Kreiss
author: Jens Lorenz
publication date: 2001-06-05T00:00:00Z
review text: The authors investigate the role played by resolvent estimates for the stability of ordinary and parabolic equations. In particular they consider the following equation in the Euclidean space \(u_t=Au + f(u)\) where \(A\) is a linear operator an Euclidean space (\(n\times n\)-matrix) and \(f\) is a nonlinear term. It is assumed that \(\text{Re }\sigma (A)<0\) where \(\sigma (A)\) is the spectrum of \(A\). Under various assumptions on \(f\), stability conditions are derived. Note that the authors established some resolvent estimates, which follow from Theorem 17.3.1 of the book [\textit{M. I. Gil'}, Stability of finite and infinite dimensional systems, Kluwer, Dordrecht (1998; Zbl 0916.93002)]. In addition, the equations of the type \[ u_t=u_{xx}+u_x+uu_x \] on a finite segment are investigated.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1471192
zbMATH Keywords: ordinary and parabolic equations
reviewed by: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: s101149900023
OpenAlex ID: W2059038644
cites work: Q5801898
cites work: Computing the field of values and pseudospectra using the Lanczos method with continuation
cites work: Computation of Pseudospectra by Continuation
cites work: Pseudospectra of the Convection-Diffusion Operator
cites work: Pseudospectra of Linear Operators
cites work: Q4215358
DOI: 10.1007/S101149900023
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1471192