On the Asymptotic Stability of Wave Equations Coupled by Velocities of Anti-symmetric Type

Abstract

In this paper, the authors study the asymptotic stability of two wave equations coupled by velocities of anti-symmetric type via only one damping. They adopt the frequency domain method to prove that the system with smooth initial data is logarithmically stable, provided that the coupling domain and the damping domain intersect each other. Moreover, they show, by an example, that this geometric assumption of the intersection is necessary for 1-D case.

Keywords

Wave equations / Coupled by velocities / Logarithmic stability

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