一类三阶方程奇摄动边值问题“啪”解的渐近分析

THE ASYMPTOTIC ANALYSIS TO COMPARISON SPACE STRUCTURE OF SINGULAR PETURBAION BOUNDARY VALUE PROBLEM OF A CLASS OF THIRD-ORDER EQUATION

研究了一类出现所谓“啪”解(对照空间结构)的三阶奇摄动边值问题,给出了上述问题在出现一个“啪”解时的渐近解的构造算法及其条件;采用逐步推算法,利用解在“啪”点的连续性条件,具体地找出了“啪’点,且得到了边界层函数的指数式衰减估计;最后,对在描述“啪”点主项t_0处间断的渐近解进行了修正,使其在讨论区间上二次连续可微,得到了误差估计定理。

In this paper, we make research on singular peturbation boundary value problem of a class of third-order equation,in which the so-called 'blow-up' solution oc-curs. We also give the structure and its condition of the asymptotic solution when there ex-ists one 'blow-up' solution of the problem above. We find the 'blow-up' point by means of gradual calculation and contionuity condition of the solution at 'blow-up' point. Moreover, we obtain the degenerate estimate of the boundary layer function in exponential expression. Then, we modify the asymptotic solutions which are discontinous at the main term of 'blow-up' point,so that the solutions are continuously differentiable for two times in the interval discussed. Finally, we get the theorem of error estimate.