The effect of  the wave speeds and the frictional damping terms  on the decay rate of the Bresse system

Abdelaziz Soufyane; Belkacem Said-Houari

doi:10.3934/eect.2014.3.713

Article Contents

2014, Volume 3, Issue 4: 713-738. Doi: 10.3934/eect.2014.3.713

This issue Previous Article On the threshold for Kato's selfadjointness problem and its $L^p$-generalization Next Article

The effect of the wave speeds and the frictional damping terms on the decay rate of the Bresse system

Abdelaziz Soufyane^1, and
Belkacem Said-Houari^1,

1.
ALHOSN University, Mathematics and Natural Sciences Department, PO Box 38772, Abu Dhabi

Received: July 2014

Revised: September 2014

Published: December 2014

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Abstract

In this paper, we consider the Bresse system with frictional damping terms. We investigated the relationship between the frictional damping terms, the wave speeds of propagation and their influence on the decay rate of the solution. We proved that in many cases the solution enjoys the decay property of regularity-loss type. We introduced a new assumption on the wave speeds that controls the behavior of the solution of the Bresse system. In addition, when the coefficient $l $ goes to zero, we showed that the solution of the Bresse system decays faster than the one of the Timoshenko system. This result seems to be the first one to give the decay rate of the solution of the Bresse system in unbounded domain.

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Mathematics Subject Classification: 35B35, 35L55, 74D05, 93D15, 93D20.

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