奇摄动向量问题的边界层和内层现象

本文考虑非线性向量边值问题:εy″=f(x,y,z,y',ε), y(0)=A₁ y(1)=B₁ εz″=f(x,y,z,z',ε), z(0)=A₂ z(1)=B₂其中ε是正的小参数,0≤x≤1,f,g是R4中的连续函数。在适当的假设下,利用微分不等式理论,我们证明了上述问题的解的存在性,并得到包括边界层和内层在内的解的估计.

Boundary and Interior Layer Behavior for Singularly Perturbed Vector Problem

In this paper, we consider the vector nonlinear boundary value problem:εy″=f(x,y,z,y',ε), y(0)=A₁ y(1)=B₁ εz″=f(x,y,z,z',ε), z(0)=A₂ z(1)=B₂ where ε>0 is a small parameter,0≤x≤1 f and g are continuous functions in R4. Under appropriate assumptions, by means of the differential inequalities, we demonstrate the existence and estimation, involving boundary and interior layers, of the solutions to the above problem.