一类奇摄动积分微分方程边值问题

A class of singularly perturbed integral differential equation boundary value problem

研究了一类具有混合边界条件的奇摄动二阶积分微分方程边值问题。首先,使用伸长变量和边界层矫正法,构造出了奇摄动问题的形式渐近解;然后,运用微分不等式理论,证明了形式渐近解的一致有效性,并得出了解得任意阶的一致有效展开式。

This paper studies a class of singularly perturbed two order integral differential equation boundary value problem with mixed boundary conditions. Using the stretched variable and the method of boundary layer correction, the formal asymptotic expansion for the solution of the problem is obtained. And then, the uniform validity of solution is proved and the uniform valid asymptotic expansions of arbitrary order are obtained by using the theories of differential inequalities.