On the Asymptotic Stability of Wave Equations Coupled by Velocities of Anti-symmetric Type
대칭형 속도가 결합된 파동 방정식의 점근적 안정성에 대하여
Sobre la estabilidad asintótica de las ecuaciones de onda acopladas por velocidades de tipo antisimétrico
Sur la stabilité asymptotique des équations d'onde couplées par des vitesses de type antisymétrique
Об асимптотической устойчивости волновых уравнений, связанных скоростями антисимметричного типа
Yan Cui ¹, Zhiqiang Wang 王志强 ²
¹ Department of Mathematics, Jinan University, Guangzhou, 510632, China
中国 广州 暨南大学数学系
² School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China
中国 上海 复旦大学数学科学学院 上海市现代应用数学重点实验室
Chinese Annals of Mathematics, Series B, 12 November 2021

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.
Chinese Annals of Mathematics, Series B_1
Chinese Annals of Mathematics, Series B_2
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