含无界时滞的微极流方程组稳态解的稳定性  

Stability of Stationary Solutions to Micropolar Fluid Equations With Unbounded Delay

作　　者：易卢燕 刘国威 YI Luyan;LIU Guowei(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China;School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]上海交通大学数学科学学院,上海200240

出　　处：《应用数学和力学》2025年第4期551-562,共12页Applied Mathematics and Mechanics

基　　金：中国博士后科学基金(2022M722105);重庆市自然科学基金(面上项目)(CSTB2024NSCQ-MSX1089);重庆市教育委员会科学技术研究基金(KJQN202200563)。

摘　　要：利用四种不同的技术结合稳定性理论研究了含无界时滞的微极流方程组稳态解的稳定性.结果表明,当无界时滞函数关于时间连续可微时,非平凡稳态解具有局部稳定性和平凡稳态解具有渐近稳定性;当无界时滞函数关于时间仅连续时,非平凡稳态解具有全局稳定性;当无界时滞为比例时滞时,平凡稳态解具有多项式稳定性.The stability of stationary solutions to micropolar fluid equations with unbounded delay was studied through combination of 4 different techniques with the stability theory.The results show that,when the unbounded delay function is continuously differentiable with respect to time,the nontrivial stationary solution will be locally stable and the trivial stationary solution will be asymptotically stable;when the unbounded delay function is only continuous with respect to time,the nontrivial stationary solution will be globally stable;when the unbounded delay is a proportional delay,the trivial stationary solution will be polynomially stable.

关 键 词：微极流 无界时滞 稳态解 稳定性 渐近稳定性 多项式稳定性 

分 类 号：O29[理学—应用数学]