| 倪明康,古尔曼.奇摄动问题中阶梯状解的缝接法[J].数学研究及应用,2012,32(1):26~32 |
| 奇摄动问题中阶梯状解的缝接法 |
| Sewing Connection of Step-Step Solution for Singularly Perturbed Problems |
| 投稿时间：2010-01-18 修订日期：2010-04-27 |
| DOI：10.3770/j.issn:2095-2651.2012.01.004 |
| 中文关键词: 缝接法 内层现象 渐近展开式. |
| 英文关键词:sewing connection internal layer phenomenon asymptotic expansion. |
| 基金项目:国家自然科学基金(Grant Nos.11071075;11171113),俄罗斯基础研究基金(Grant No.12-01-00256),国家自然科学基金中国科学院知识创新工程资助(Grant Nos.30921064; 90820307),上海市自然科学基金(Grant No.10ZR1409200),上海高校计算科学E-研究院交大研究所(Grant No.E03004). |
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| 中文摘要: |
| 针对奇摄动问题中的复杂内层现象,其中包括空间对照结构(阶梯状解和脉冲状解),角层现象和方程右端不连续情况, 作者提出了用缝接法进行处理.它是以两点奇摄动纯边界层问题为基础的,通过对轨道的光滑缝接而得到整个区间上的一致有效渐近解.用缝接法不但可以证明解的存在性,而且可以处理高维奇摄动内层问题. |
| 英文摘要: |
| In view of singularly perturbed problems with complex inner layer phenomenon, including contrast structures (step-step solution and spike-type solution), corner layer behavior and right-hand side discontinuity, we carry out the process with sewing connection. The presented method of sewing connection for singularly perturbed equations is based on the two points singularly perturbed simple boundary problems. By means of sewing orbit smoothness, we get the uniformly valid solution in the whole interval. It is easy to prove the existence of solutions and deal with the high dimensional singularly perturbed problems. |
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