Abstract

We construct an asymptotic expansion in a small parameter of a boundary layer solution of the boundary value problem for a system of two ordinary differential equations, one of which is a second-order equation and the other is a first-order equation with a small parameter at the derivatives in both equations. Such a system arises in chemical kinetics when modeling the stationary process in the case of fast reactions and in the absence of diffusion of one of the reacting substances. A significant feature of the studied problem is that one of the equations of the degenerate system has a triple root. This leads to a qualitative difference in the boundary layer component of the solution compared with the case of simple (single) roots of degenerate equations. The boundary layer becomes multizonal, and the standard algorithm for constructing the boundary layer series turns out to be unsuitable and is replaced with a new algorithm.

中文翻译：

---

奇异微扰部分耗散方程组

摘要

我们构造两个常微分方程组的边值问题的边界层解的小参数中的渐近展开式，其中一个是二阶方程，另一个是具有小参数的一阶方程在两个方程的导数处。当在快速反应的情况下并且在没有反应物质之一的扩散的情况下对静止过程进行建模时，在化学动力学中出现这样的系统。所研究问题的一个显着特征是退化系统的方程之一具有三重根。与简并方程的简单（单）根的情况相比，这导致解的边界层分量存在质的差异。边界层变成多区域的，