带有阻尼项小周期椭圆边值问题的高阶三尺度渐近分析

The higher-order three-scale asymptotic analysis for small periodic elliptic boundary value problem with damping term

运用高阶三尺度方法构造带有阻尼项小周期椭圆边值问题解的高阶三尺度渐近展开式,得到均匀化系数和均匀化方程.基于构造的三尺度渐近展开式,定义二阶双尺度解、低阶三尺度解和高阶三尺度解,分析它们与高阶三尺度近似解之间的误差.根据误差分析,得到高阶三尺度解更逼近于近似解的结论.

By applying high-order three-scale method,the high-order three-scale asymptotic expansion for the solution of small periodic elliptic boundary value problem with damping term is constructed and the homogenization constants and equation are obtained.Based on the constructed three-scale asymptotic expansion,the second-order two-scale solution,the low-order three-scale solution and the high-order three-scale solution are defined,and the errors between them and the high-order three-scale approximate solution are analyzed.According to the error analysis,the conclusion is that the high-order three-scale solution is closer to the approximate solution.