Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping.
type: Item
instance of: scholarly article
title: Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping.
zbMATH Open document ID: 1161.35437
author: J. S. Prates Filho
author: M. M. Cavalcanti
author: V. N. Domingos Cavalcanti
author: J. A. Soriano
published in: Differential and Integral Equations
publication date: 2003-03-13T00:00:00Z
review text: The authors consider the viscoelastic problem with nonlinear boundary damping in a bounded and star-shaped domain of with smooth boundary. The main results are devoted to the global existence of strong and weak solutions of the problem and the uniform decay (either exponential or algebraic) of the energy related to the problem under suitable assumptions. The existence is proved by means of the Faedo-Galerkin method, and the asymptotic behavior is shown by making use of the multiplier technique combined with integral inequalities due to \textit{V. Komornik} [Exact controllability and stabilization. The multiplier method. Research in Applied Mathematics. 36. Chichester: Wiley. Paris: Masson (1994; Zbl 0937.93003)].
reviewed by: Grzegorz Karch
Mathematics Subject Classification ID: 35Lxx
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 74Dxx
zbMATH DE Number: 1832808
zbMATH Keywords: viscoelastic problem
zbMATH Keywords: nonlinear boundary damping
zbMATH Keywords: decay of energy
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1832808