Stability for a class of semilinear parabolic equations
type: Item
instance of: scholarly article
title: Stability for a class of semilinear parabolic equations
zbMATH Open document ID: 0824.34071
author: Anna Buttu
published in: Differential and Integral Equations
publication date: 1995-11-09T00:00:00Z
review text: A class of semilinear initial value problems in a general Banach space \(X\), \(u'(t)= Au(t)+ f(u(t))\), \(t> 0\), \(u(0)= u_ 0\), is considered, where \(A: D(A)\subset X\mapsto X\) is a sectorial operator and \(f\) is a sufficiently regular nonlinear function defined in an intermediate space \(X_ \alpha\) between \(X\) and \(D(A)\), with \(f(0)= 0\). It is supposed that \(\| e^{tA}\|_{L(X)}\leq M_ 0\), \(\| te^{tA}\|_{L(X)}\leq M_ 1\), \(t> 0\). Under suitable growth assumptions on \(f\) is a global existence and asymptotic decay theorem proved in the case where the initial datum is small in \(X_ \alpha\). The used methods are: method of contraction and method of a priori estimates. The abstract results are applied to some nonlinear evolution problems of the second and fourth order.
reviewed by: Josef Diblík
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 763459
zbMATH Keywords: semilinear initial value problems
zbMATH Keywords: Banach space
zbMATH Keywords: sectorial operator
zbMATH Keywords: global existence
zbMATH Keywords: asymptotic decay
zbMATH Keywords: nonlinear evolution problems of the second and fourth order
MaRDI profile type: Publication
Recommended article: Stabilisation of parabolic semilinear equations
Recommended article: Stabilizing Semilinear Parabolic Equations
Recommended article: Some stability results for perturbed semilinear parabolic equations
Recommended article: Stability for semilinear parabolic equations with noninvertible linear operator
Recommended article: Stability and instability of solutions of semilinear problems
Recommended article: Stability for semilinear parabolic problems in \(L_2\) and \(W^{1,2}\)
Recommended article: Stability of solutions of quasilinear parabolic equations
Recommended article: Stability in semilinear problems
Recommended article: Stability for degenerate parabolic equations
Recommended article: Stability and instability for semilinear parabolic equations with free boundary conditions
description: scientific article; zbMATH DE number 763459