| 摘要: |
| 研究了一类快双分子反应模型中具有快慢变量的Tichonov系统. 通过应用边界层函数法、缝接法以隐函数定理, 得到了对于充分小的μ在退化解附近原问题解的存在性和μ对原问题解的渐近性态的影响, 同时构造了系统解的渐近表达式. |
| 关键词: 时滞微分方程 奇摄动 渐近展开式 |
| DOI： |
| 分类号: |
| 基金项目: |
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| Existence and rigorous asymptotics of the solutions of a class of singularly perturbed delay-differential equations |
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WANG Na
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College of Mathematics and Science, Shanghai Normal University
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| Abstract: |
| We consider the singularly perturbed delayed systems of Tichonov′s type with fast and slow variables in a fast bimolecular reaction model. By means of the boundary layer function method, sewing connection and the implicit function theorem, we prove the existence of the solutions of our problems near the degenerate solution for a sufficiently small μ and determine its asymptotic behavior in μ. Meanwhile, the asymptotic expression of the systems is also constructed. |
| Key words: delay-differential equations singular perturbation asymptotic expression |
