| 具有超抛物型极限方程的非线性奇摄动反应扩散问题 |
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| 引用本文： | 莫嘉琪.具有超抛物型极限方程的非线性奇摄动反应扩散问题[J].数学进展,2008,37(1):85-91. |
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| 作者姓名： | 莫嘉琪 |
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| 作者单位： | 安徽师范大学数学系,芜湖,安徽,241000;湖州师范学院数学系,湖州,浙江,313000;上海高校计算科学E-研究院上海交通大学研究所,上海,200240 |
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| 基金项目： | 国家自然科学基金
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国家重点基础研究发展计划(973计划)
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中国科学院基金
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上海市教委资助项目 |
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| 摘 要： | 讨论了一类具有超抛物型方程的反应扩散问题.首先,证明了比较定理.其次,构造了形式渐近解.然后,利用微分不等式方法,研究了问题解的存在、唯一性和渐近性态.最后得到了原问题解的渐近展开式.
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| 关 键 词： | 超抛物型方程 奇摄动 反应扩散 渐近性态 比较定理 ultra parabolic equation singular perturbation reaction diffusion asymptotic behavior comparison theorem 抛物型 极限方程 线性奇摄动 反应 扩散问题 Equations Parabolic Ultra Problems Reaction Diffusion Singularly Perturbed valid asymptotic behavior expansion of the solution original uniqueness problems existence differential inequalities method |
| 文章编号： | 1000-0917（2008）01-0085-07 |
| 收稿时间： | 2006-06-05 |
| 修稿时间： | 2006年6月5日 |
Nonlinear Singularly Perturbed Reaction Diffusion Problems With Ultra Parabolic Limiting Equations |
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| MO Jiaqi.Nonlinear Singularly Perturbed Reaction Diffusion Problems With Ultra Parabolic Limiting Equations[J].Advances in Mathematics,2008,37(1):85-91. |
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| Authors: | MO Jiaqi |
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| Abstract: | The reaction diffusion problems with ultra parabolic equations are considered. Firstly, a comparison theorem is proved. Secondly, a formal asymptotic solution is constructed. Thirdly, by using the differential inequalities method, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied. Finally, the uniformly valid asymptotic expansion of the solution for the original problem is obtained. |
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| Keywords: | ultra parabolic equation singular perturbation reaction diffusion asymptotic behavior comparison theorem |
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