一类四阶非线性奇摄动方程的边值问题

A class of boundary value problems for four-order nonlinear singular perturbation equation

利用匹配渐近展开法,讨论了一类四阶非线性方程的具有两个边界层的奇摄动边值问题.引进伸长变量,根据边界条件与匹配原则,在一定的可解性条件下,给出了外部解和左右边界层附近的内层解,得到了该问题的二阶渐近解,并举例说明了这类非线性问题渐近解的存在性.

Using the matching asymptotic expansion method, a class of singu- larly perturbed boundary value problems with two boundary layers for forth-order nonlinear equation is studied. Introducing the stretched variables, according to the boundary conditions and the matching principle, under the definite solvabil- ity conditions, the outer solution and the interior solution near the left and right boundary layers are given. The asymptotic solution with second-order for the prob- lem is obtained. The existence of the solution for this class of nonlinear problems is illustrated by an example.