带强阻尼的 Boussinesq 方程时间周期解  

The Time Periodic Solutions for theBoussinesq Equation with StrongDamping

作　　者：胥浩 

机构地区：[1]重庆师范大学,数学科学学院,重庆

出　　处：《理论数学》2023年第5期1173-1189,共17页Pure Mathematics

摘　　要：本文研究了带强阻尼的 Boussinesq 方程时间周期解问题,通过对解算子的谱分析和压缩映射原理证明了在周期外力具有某种小性时,带强阻尼的 Boussinesq 方程时间周期解的存在唯一性, 并且解的周期与外力项的周期相同。In this paper, the problem of time periodic solutions for the Boussinesq equation with strong damping is studied. When the periodic external force has some small property,the existence and uniqueness of the time-periodic solutions for the Boussinesq equation with Strong damping are proved by spectral analysis of the solution operator and the principle of compression mapping. Moreover, the period of the solution is the same as that of the external force term.

关 键 词：Boussinesq 方程 强阻尼 时间周期解 存在唯一性 

分 类 号：O17[理学—数学]