Stability of a star-shaped network with local Kelvin-Voigt damping and\n non-smooth coefficient at interface

2020/06/24 by Fathi Hassine, Hassine, Fathi
Computer Science · Engineering · Mathematics · #35B35 #35B40 #93D20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2006.14949

openalex publication_date 2020/06/24 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the stability problem of a star-shaped network of\nelastic strings with a local Kelvin-Voigt damping. Under the assumption that\nthe damping coefficients have some singularities near the transmission point,\nwe prove that the semigroup corresponding to the system is polynomially stable\nand the decay rates depends on the speed of the degeneracy. This result\nimproves the decay rate of the semigroup associated to the system on an earlier\nresult of Z.~Liu and Q.~Zhang in citeLZ involving the wave equation with\nlocal Kelvin-Voigt damping and non-smooth coefficient at interface.\n

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