Decay for the solutions of nonlinear abstract damped evolution equations with applications to partial and ordinary differential systems
type: Item
instance of: scholarly article
title: Decay for the solutions of nonlinear abstract damped evolution equations with applications to partial and ordinary differential systems
zbMATH Open document ID: 1004.35101
author: M. Cesarina Salvatori
author: Enzo Vitillaro
published in: Differential and Integral Equations
publication date: 2000-05-29T00:00:00Z
review text: The paper is devoted to the investigation of general abstract evolution equations \([P(u'(t))]'+A(u(t)) + Q(t,u(t),u'(t)) + F(u(t))=0\), where \(A,F,P\) and \(Q\) are nonlinear operators in appropriate Banach spaces, and \(t>0\) is the time variable. Equations of the above form are described according to the asymptotic behavior of solutions. Assuming that a global solution exists, the authors derive precise decay estimates for the energy functional \(E(t)\) in each case. It is shown that the results can be applied for instance to quasilinear hyperbolic equations with nonlinear damping.
Mathematics Subject Classification ID: 35L90
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1453630
zbMATH Keywords: quasilinear hyperbolic equations
zbMATH Keywords: nonlinear damping
reviewed by: Pavel Krejč{í }
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1453630