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

2018/08/30 by Farah Abdallah, Abdallah, Farah, Yacine Chitour +5
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1808.10256

openalex publication_date 2018/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. 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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