奇摄动非线性系统的边界层与内过渡层性质

Boundary and Interior Transition Layer Behavior in Singularly Perturbed Nonlinear Systems

本文对非线性向量边值问题εy″=f(x,y,y′),-1<x<1, y(-1,e)=A,y(1,ε)=B,应用微分不等式理论研究了当ε→0^+时解的存在性和渐近性质,对充分小的ε>0,在适当的假设下,证明其解的一些分量呈边界层性态,而另一些分量呈内单调过渡层性态。

The existence and asympototic behavior as ε→0^+ of solutions of the nonlinear vector boundary value problem εy″= f(x, y, y′), -1<x<1, y(-1, ε)=A, y(1, e)=B are studied using the theory of differential inequalities. For ε>0 sufficiently small, under the proper assumpations, some components of the solution are shown to exhibit boundary layer behavior, and the other components to exhibit interior monotone transition layer behavior.