强耦合变系数波动方程的间接边界镇定  

Indirect Boundary Stabilization of Strongly Coupled Variable Coefficient Wave Equations

作　　者：崔佳楠 柴树根[1] Cui Jianan;Chai Shugen(School of Mathematical Sciences,Shanai University,Taiyuan 030006;Department of Mathematics,Jinzhong University,Shanai Jinzhong 030619)

机构地区：[1]山西大学数学科学学院,太原030006 [2]晋中学院数学系,山西晋中030619

出　　处：《数学物理学报(A辑)》2025年第2期389-407,共19页Acta Mathematica Scientia

基　　金：国家自然科学基金(12271316);晋中学院博士专项基金(23E00611)。

摘　　要：该文旨在研究带变系数和边界阻尼的强耦合波动方程的间接镇定.值得注意的是,系统中只有一个方程直接受到边界阻尼的影响.利用黎曼几何方法和高阶能量方法,证明了全局耦合系统的衰减速率受边界条件类型的影响.研究结果表明,当无阻尼方程具有Dirichlet边界条件时,系统表现出指数稳定性,而当无阻尼方程具有Neumann边界条件时,系统仅有多项式稳定性.最后,在Dirichlet和Neumann边界条件下建立了局部耦合系统的指数稳定性.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.

关 键 词：间接镇定 强耦合 非均匀介质 边界反馈 

分 类 号：O231.4[理学—运筹学与控制论]