具有无穷大边界值的二阶拟线性奇摄动Robin问题的双边界层

Doubled Boundary Layers of Robin Problems with Infinite Boundary Values for Singularly Perturbed Quasi-linear Differential Equations

研究一类具有无穷大边界值的二阶拟线性奇摄动Robin边值问题的双边界层现象.基于边界层校正的思想,构造了左右端点附近的边界层函数(包括指数型与代数型),得到了该问题一致有效的渐近解;基于微分不等式理论,证明了该问题解的存在性,给出了渐近解关于精确解的误差估计.一个典型的算例验证了所得结果的正确性.

Doubled boundary layers phenomenon of Robin problems with infinite boundary values for second-order singularly perturbed quasi-linear differential equations is studied.Based on the technique of boundary layer correction,the boundary layer functions（including the exponential and algebraic types） at the ended points are constructed and hence the asymptotic approximation of solutions is obtained.Differential inequality is then applied to derive the existence of solution and the error estimate between the asymptotic and the exact solutions.An example is performed to verify the correctness of the obtained results.