Stability of a damped wave equation on an infinite star-shaped network | Zendy

Ahmed Bchatnia | Zendy; Amina Boukhatem | Zendy

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Stability of a damped wave equation on an infinite star-shaped network

Author(s) -

Ahmed Bchatnia,

Amina Boukhatem

Publication year - 2022

Publication title -

evolution equations and control theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.665

H-Index - 19

eISSN - 2163-2480

pISSN - 2163-2472

DOI - 10.3934/eect.2022024

Subject(s) - star (game theory) , stability (learning theory) , domain (mathematical analysis) , physics , energy (signal processing) , wave equation , damped wave , frequency domain , exponential stability , mathematical analysis , mathematics , energy method , stability theory , mathematical physics , computer science , quantum mechanics , nonlinear system , machine learning

In this paper, we study the stability of an infinite star-shaped network of a linear viscous damped wave equation. We prove that, under some conditions, the whole system is asymptotically stable. Moreover we give a decay rate of the energy of the solution. Our technique is based on a frequency domain method.

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