| 摘要: |
| 本文研究了不满足Tikhnov定理中稳定性要求的一类常微分方程奇摄动边值问题.利用边界层函数法以及微分不等式理论,分别构造了渐进解的形式和证明了解的存在性和渐近解一致有效性并进行了余项估计,得出了该类问题边界层代数式衰减的结论. |
| 关键词: 奇摄动 渐近解 代数衰减 |
| DOI： |
| 分类号:O175.14 |
| 基金项目:国家自然科学基金，上海市教育委员会E-研究院建设项目，地理信息科学教育部重点实验室开放课题，上海市重点学科建设项目 |
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| SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH ALGEBRAIC DECAY BOUNDARY LAYER |
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NI Ming-kang,DING Hai-yun
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NI Ming-kang1,2,DING Hai-yun2(1.Dept.of Math.,East China Normal University,Shanghai 200062,China)(2.Division of Computational Science,E-Institute of Shanghai Universities,Shanghai JiaotongUniversity,Shanghai 200031,China)
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| Abstract: |
| In this article,a class of boundary value problems for the singularly perturbed ordinary differential equations with the stability condition of Tikhnov theorem fails is considered.The corresponding asymptotic solutions are constructed by the method of boundary layer function.By using theory of differential inequality,the existence of the solution and the uniform validity of its asymptotic solutions are proved and the remainder estimate is derived.The algebraic decay of boundary layer for this class of probl... |
| Key words: singular perturbation asymptotic solutions algebraic decay |
