一类奇摄动薄板弯曲问题的匹配渐近解

Matched asymptotic solution to a class of singularly perturbed thin plate bending problem

研究了一类薄板弯曲问题.对四阶奇摄动边值问题,引入伸长变量,构造边界附近的内层解,然后与外部解匹配.最后用合成展开式理论,得到了原问题的的渐近解.

The thin plate-bending problem is studied.Introducing the stretched variables,the internal layer solutions near the boundary are constructed for the fourth order singularly perturbed boundary problem.Then matching the solutions with outer solution and using the theory of the composite expansion,the asymptotic solution is obtained finally.