Stability to weak dissipative Bresse system
type: Item
instance of: scholarly article
title: Stability to weak dissipative Bresse system
zbMATH Open document ID: 1209.35018
author: Fatiha Alabau-Boussouira
author: D. S. Almeida Júnior
author: Jaime E. Muñoz Rivera
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-11-22T00:00:00Z
review text: The paper deals with the Bresse system with frictional dissipation working only on the angle displacement. The Bresse system is also known as the circular arch problem. It is given by the coupled system of three second order hyperbolic equations. The authors have proved that, the system is not exponentially stable, in general. Namely, it is shown that the considered system is exponentially stable if and only if the velocities of waves propagations are equals. This never happens in the practice. Thus we never have exponential stability. When the velocities are different, it is proved that the solutions decay polynomially to zero, with rates that depends on the initial data and some relationships between the coefficients. A numerical result to verify the analytical results is suggested.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 5817871
zbMATH Keywords: Bresse system
zbMATH Keywords: lack of exponential decay
zbMATH Keywords: semigroups
zbMATH Keywords: finite difference
reviewed by: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.07.046
OpenAlex ID: W1975230327
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DOI: 10.1016/J.JMAA.2010.07.046
description: scientific article; zbMATH DE number 5817871