Piecewise multiplier method and nonlinear integral inequalities for Petrowsky equation with nonlinear dissipation
type: Item
instance of: scholarly article
title: Piecewise multiplier method and nonlinear integral inequalities for Petrowsky equation with nonlinear dissipation
zbMATH Open document ID: 1117.34054
author: Fatiha Alabau-Boussouira
published in: Journal of Evolution Equations
publication date: 2007-01-24T00:00:00Z
review text: The author proves that the piecewise multiplier method introduced by \textit{K. Liu} [SIAM J. Control Optimization 35, 1574--1590 (1997; Zbl 0891.93016)] and \textit{P. Martinez} [Rev. Mat. Complut. 12, 251--283 (1999; Zbl 0940.35034)] for the wave equation can be extended to the Petrowsky equation. Some recent results of the author are also applied in order to obtain decay rate estimates for the energy, without specifying the growth of the nonlinear dissipation close to the origin by means of convex properties and nonlinear integral inequalities for the energy of the solutions.
reviewed by: Adina Luminiţa Sasu
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35L90
zbMATH DE Number: 5118017
zbMATH Keywords: nonlinear dissipation
zbMATH Keywords: locally distributed mapping
zbMATH Keywords: hyperbolic equations
zbMATH Keywords: second order evolution equation
MaRDI profile type: Publication
full work available at URL: s00028-005-0230-y
OpenAlex ID: W2081929551
DOI: 10.1007/S00028-005-0230-Y
description: scientific article; zbMATH DE number 5118017