强耦合变系数波动方程的间接边界镇定

Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (2): 389-407.

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Indirect Boundary Stabilization of Strongly Coupled Variable Coefficient Wave Equations

Cui Jianan^1,²(),Chai Shugen^1,^*()

¹School of Mathematical Sciences, Shanxi University, Taiyuan 030006
²Department of Mathematics, Jinzhong University, Shanxi Jinzhong 030619

Received:2024-05-28 Revised:2024-10-30 Online:2025-04-26 Published:2025-04-09
Contact: Shugen Chai E-mail:1391958885@qq.com;sgchai@sxu.edu.cn
Supported by:
NSFC(12271316);Jinzhong University Research Funds for Doctor(23E00611)

Abstract

Abstract:

In this paper, the indirect stabilization of strongly coupled wave equations with variable coefficients and boundary damping is studied. It is important to note that only one equation in the system is directly affected by boundary damping. By using Riemannian geometry method and higher order energy method, it is proved that the decay rate of the globally coupled system is affected by the type of boundary conditions. The results show that when the undamped equations have Dirichlet boundary conditions, the system exhibits exponential stability, while when the undamped equations have Neumann boundary conditions, the system has only polynomial stability. Finally, the exponential stability of the locally coupled system is established under Dirichlet and Neumann boundary conditions.

Key words: indirect stabilization, strong coupling, inhomogeneous media, boundary feedback

CLC Number:

O231.4

Cui Jianan,Chai Shugen. Indirect Boundary Stabilization of Strongly Coupled Variable Coefficient Wave Equations[J].Acta mathematica scientia,Series A, 2025, 45(2): 389-407.

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Indirect Boundary Stabilization of Strongly Coupled Variable Coefficient Wave Equations

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