一类带有阻尼项的小周期结构热力耦合问题的均匀化分析

Homogenization Analysis of a Class of Thermodynamic Coupling Problems for Small Periodic Structures with Damping Terms

以双尺度理论为基础研究了一类带有阻尼项的小周期结构热力耦合问题,提出了其偏微分方程组的均匀化方法,通过构造适当的单胞函数,利用双尺度渐近展开方法得到了该方程组的均匀化系数及均匀化方程组,证明该方程组解的存在性和唯一性。

Based on the double scale theory,a class of thermodynamic coupling problems for small periodic structures with damping terms is studied.The homogenization method of partial differential equations is proposed.By being constructed appropriate cell functions,the homogenization coefficient and homogenization equations of the system are obtained by the double scale asymptotic expansion method.The existence and uniqueness of the solutions of the equations are proved.