| 一类三阶方程奇摄动边值问题“啪”解的渐近分析 |
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| 引用本文： | 李文龙.一类三阶方程奇摄动边值问题“啪”解的渐近分析[J].武汉大学学报(理学版),1994(6). |
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| 作者姓名： | 李文龙 |
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| 作者单位： | 中国人民解放军军事经济学院基础部 武汉430035 |
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| 基金项目： | 国家教委博士学科点专项科研基金资助的课题 |
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| 摘 要： | 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。
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| 关 键 词： | 奇摄动 “啪”解 渐近分析 |
THE ASYMPTOTIC ANALYSIS TO COMPARISON SPACE STRUCTURE OF SINGULAR PETURBAION BOUNDARY VALUE PROBLEM OF A CLASS OF THIRD-ORDER EQUATION |
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| Li Wenlong.THE ASYMPTOTIC ANALYSIS TO COMPARISON SPACE STRUCTURE OF SINGULAR PETURBAION BOUNDARY VALUE PROBLEM OF A CLASS OF THIRD-ORDER EQUATION[J].JOurnal of Wuhan University:Natural Science Edition,1994(6). |
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| Authors: | Li Wenlong |
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| Abstract: | 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. |
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| Keywords: | singular peturbation "blow-up" solution asymptotic analysis |
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