Stabilization of a locally transmission problems of two strongly-weakly coupled wave systems

2023/10/12 by Ahmedi, Wafa, Aissa, Akram Ben
#35Q74 #74J30 #93D15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.08290

Abstract

In this paper, we embark on a captivating exploration of the stabilization of locally transmitted problems within the realm of two interconnected wave systems. To begin, we wield the formidable Arendt-Batty criteria\citeAW to affirm the resolute stability of our system. Then, with an artful fusion of a frequency domain approach and the multiplier method, we unveil the exquisite phenomenon of exponential stability, a phenomenon that manifests when the waves of the second system synchronize their propagation speeds. In cases where these speeds diverge, our investigation reveals a graceful decay of our system's energy, elegantly characterized by a polynomial decline at a rate of t^-1.

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