奇摄动向量问题的边界层和内层现象

基金项目: 国家自然科学基金资助的项目

Boundary and Interior Layer Behavior for Singularly Perturbed Vector Problem

摘要: 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.
- 奇摄动 /
- 微分不等式 /
- 边界层 /
- 内层
Abstract: 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.
- singular perturbation /
- differential inequality /
- boundary layer /
- inner layer

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