Stabilization of coupled wave equations with viscous damping on\n cylindrical and non-regular domains: Cases without the geometric control\n condition

2021/11/29 by Mohammad Akil, Haidar Badawi, Akil, Mohammad +5
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.14554

openalex publication_date 2021/11/29 · openalex created_date 2022/11/07 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the direct and indirect stability of locally\ncoupled wave equations with local viscous damping on cylindrical and\nnon-regular domains without any geometric control condition. If only one\nequation is damped, we prove that the energy of our system decays polynomially\nwith the rate t^-\(1)/(2) if the two waves have the same speed of\npropagation, and with rate t^-\(1)/(3) if the two waves do not propagate\nat the same speed. Otherwise, in case of two damped equations, we prove a\npolynomial energy decay rate of order t^-1.\n

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