Stability in fully nonlinear parabolic equations
type: Item
instance of: scholarly article
title: Stability in fully nonlinear parabolic equations
zbMATH Open document ID: 0832.35069
DOI: 10.1007/BF00375654
author: Alessandra Lunardi
published in: Archive for Rational Mechanics and Analysis
publication date: 1995-07-18T00:00:00Z
review text: The stability of the zero solution of a class of nonlinear evolution equations in a Banach space is studied. After stating a local existence result and the principle of linearized stability, the author studies the critical case, giving sufficient conditions for stability. The results are applied to second-order fully nonlinear parabolic equations in \([0,+\infty[\times \mathbb{R}^n\).
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 58D25
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 775513
zbMATH Keywords: abstract parabolic equation
zbMATH Keywords: principle of linearized stability
reviewed by: A. A. Martynyuk
MaRDI profile type: Publication
cites work: Nonlinear analytic semiflows
cites work: Generation of Analytic Semigroups by Elliptic Operators with Unbounded Coefficients
cites work: Equations d'évolution abstraites non linéaires de type parabolique
cites work: Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space
cites work: The principle of linearized stability for quasilinear parabolic evolution equations
cites work: Q5547841
cites work: Geometric theory of semilinear parabolic equations
cites work: Q5187597
cites work: Long-time behavior of solutions to nonlinear evolution equations
cites work: Q3712656
cites work: Asymptotic exponential stability in quasilinear parabolic equations
cites work: On the evolution operator for abstract parabolic equations
cites work: Analytic semigroups and optimal regularity in parabolic problems
cites work: Fully nonlinear integrodifferential equations in general Banach space
cites work: Q3712926
cites work: Stability for semilinear parabolic equations with noninvertible linear operator
cites work: The linearization principle for the stability of solutions of quasilinear parabolic equations. I
cites work: Global existence of small solutions to a class of nonlinear evolution equations
cites work: Q4066072
cites work: On the abstract Cauchy problem of parabolic type in spaces of continuous functions
cites work: Q4169288
cites work: Existence and non-existence of global solutions for a semilinear heat equation
cites work: Global existence for nonlinear parabolic equations
cites work: Remarks on global existence for nonlinear parabolic equations
full work available at URL: https://doi.org/10.1007/bf00375654
OpenAlex ID: W1988209026
description: scientific article; zbMATH DE number 775513