Convergence in smooth strongly monotone flows defined by semilinear parabolic equations
type: Item
instance of: scholarly article
title: Convergence in smooth strongly monotone flows defined by semilinear parabolic equations
zbMATH Open document ID: 0684.34064
DOI: 10.1016/0022-0396(89)90115-0
published in: Journal of Differential Equations
publication date: 1989-01-01T00:00:00Z
review text: After the experimental discovery of oscillatory evolutions in processes described by parabolic systems, two approaches have been used to determine asymptotic properties of the corresponding flows: linearization near known equilibria, and imposition of `suitable' smoothness conditions on the form of equations, allowing a comparison argument in a `suitable' space. The author uses the latter approach to establish an order relation for bounded trajectories, but cannot dispense with linearizations. Although the number of hypotheses and restrictions is quite large, the author claims that they apply to models of experimental processes. This claim is not substantiated by a comparison of `suitable' and realistic spaces.
Mathematics Subject Classification ID: 34G99
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4120604
zbMATH Keywords: strong comparison principle
zbMATH Keywords: oscillatory evolutions
zbMATH Keywords: parabolic systems
author: Peter Poláčik
reviewed by: Igor Gumowski
MaRDI profile type: Publication
full work available at URL: 0022-0396(89)90115-0
OpenAlex ID: W2132772751
cites work: On stabilization of discrete monotone dynamical systems
cites work: Q3027518
cites work: Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
cites work: On abstract parabolic fundamental solutions
cites work: Dual semigroups and second order linear elliptic boundary value problems
cites work: Q4146134
cites work: Q3948194
cites work: Q5630031
cites work: Q3333766
cites work: Geometric theory of semilinear parabolic equations
cites work: Differential equations and convergence almost everywhere in strongly monotone semiflows
cites work: Stability and convergence in strongly monotone dynamical systems.
cites work: Q5526485
cites work: Q5732050
cites work: Asymptotic behavior of some nonlinear heat equations
cites work: Structure of the set of steady-state solutions and asymptotic behavior of semilinear heat equations
cites work: Q3334299
cites work: Q3814124
cites work: Convergence of solutions of one-dimensional semilinear parabolic equations
cites work: Group actions on strongly monotone dynamical systems
cites work: Stability for semilinear parabolic equations with noninvertible linear operator
cites work: Q5533735
cites work: Norms and Domains of the Complex Powers A B z
cites work: Interpolation in $L^{p}$ with boundary conditions
cites work: Asymptotically stable equilibria for monotone semiflows
cites work: Q4169288
cites work: Q5640108
cites work: Q5185568
description: scientific article; zbMATH DE number 4120604