条件稳定拟线性二阶方程组的奇摄动Dirichlet问题

Conditionally Stable Dirichlet Problem of Quasilinear Singularly Perturbed Second Order System

本文讨论了奇摄动拟线性二阶方程组的Dirichlet问题?? 其中A(z,t)为m×m阶的条件稳定型矩阵.本文在一定条件下证明了上述问题解的存在唯一性,且可用边界层函数法将此解对ε展开至任意精确度.

In this paper we consider the singularly perturbed Dirichlet problem of quasilinear System for the second order equations (d^z)/(dt^2)=A(z,t)(dz)/(dt)+B(z,t),0≤t≤1,0<ε<1, z(0,ε)=α,z(1,ε)=β where A(z, t) is a conditionally stable m×m matrix.The existence and uniqueness of solution for the problem mentioned above are proved under some conditions, and the solution can be expanded in arbitrary accuracy by the method of boundary layer functiion.