Spectral analysis and exponential or polynomial stability  of some indefinite sign damped problems

Farah Abdallah; Denis Mercier; Serge Nicaise

doi:10.3934/eect.2013.2.1

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2013, Volume 2, Issue 1: 1-33. Doi: 10.3934/eect.2013.2.1

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Spectral analysis and exponential or polynomial stability of some indefinite sign damped problems

1.
Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, Institut des Sciences et Techniques of Valenciennes, F-59313 - Valenciennes Cedex 9

Received: April 30, 2012

Revised: September 30, 2012

Published: February 2013

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Abstract

In this paper, we consider two damped wave problems for which the damping terms are allowed to change their sign. Using a careful spectral analysis, we find critical values of the damping coefficients for which the problem becomes exponentially or polynomially stable up to these critical values.

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Mathematics Subject Classification: Primary: 35L05, 35B40; Secondary: 93D20, 35P10.

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References

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