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 smo...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.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11971119,12001555)the Science and Technology Commission of Shanghai Municipality(No.19JC1420101)the Shanghai Key Laboratory for Contemporary Applied Mathematics at Fudan University(No.74120-42080001)。
文摘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.
