Optimal indirect stability of a weakly damped elastic abstract system of second order equations coupled by velocities

Farah Abdallah; Mouhammad Ghader; Ali Wehbe; Yacine Chitour

doi:10.3934/cpaa.2019125

Article Contents

2019, Volume 18, Issue 5: 2813-2842. Doi: 10.3934/cpaa.2019125

This issue Previous Article Existence, uniqueness and regularity of the solution of the time-fractional Fokker–Planck equation with general forcing Next Article Pointwise estimates of solutions to conservation laws with nonlocal dissipation-type terms

Optimal indirect stability of a weakly damped elastic abstract system of second order equations coupled by velocities

1.
Lebanese University, Faculty of Sciences 1 and EDST, KALMA, Hadath-Beirut-Lebanon
2.
Paris-Saclay University, L2S, 3 Rue Joliot Curie, Gif-sur-Yvette, France

Received: August 31, 2018

Revised: December 31, 2018

Published: March 2019

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Abstract

In this paper, by means of the Riesz basis approach, we study the stability of a weakly damped system of two second order evolution equations coupled through the velocities (see (1.1)). If the fractional order damping becomes viscous and the waves propagate with equal speeds, we prove exponential stability of the system and, otherwise, we establish an optimal polynomial decay rate. Finally, we provide some illustrative examples.

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Mathematics Subject Classification: 34G10, 35B40, 93D20.

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