Exponential stability of a general network of 1-d thermoelastic rods

Abdallah Ben Abdallah; Farhat Shel

doi:10.3934/mcrf.2012.2.1

Article Contents

2012, Volume 2, Issue 1: 1-16. Doi: 10.3934/mcrf.2012.2.1

This issue Previous Article Next Article Eventual regularity of a wave equation with boundary dissipation

Exponential stability of a general network of 1-d thermoelastic rods

Abdallah Ben Abdallah^1, and
Farhat Shel^2,

1.
Université de Sfax, Institut Supérieur d’Informatique et du Multimédia de Sfax, Pôle technologique, Route de Tunis, km 10, B.P. 242, Sfax 3021
2.
Université de Sfax, Institut Supérieur d’Informatique et du Multimédia de Sfax, Route Manzel Chaker, Km 0.5, B.P. 1172, Sfax 3018

Received: October 31, 2010

Revised: November 30, 2011

Published: February 2012

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Abstract

We consider a finite planar network of 1-$d$ thermoelastic rods using Fourier's law or Cattaneo's law for heat conduction, we show that the system is exponentially stable in the two cases.

Keywords:

Mathematics Subject Classification: 35B40, 35M10, 93D20.

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