具有边界摄动弱非线性反应扩散方程的奇摄动  

Singular Perturbation for the Weakly Nonlinear Reaction Diffusion Equation With Boundary Perturbation

作　　者：莫嘉琪[1,2,3] 张鸿庆 

机构地区：[1]安徽师范大学数学系,安徽芜湖241000 [2]湖州师范学院数学系,浙江湖州3130004 [3]上海高校计算科学E-研究院上海交通大学研究所,上海200240

出　　处：《应用数学和力学》2008年第8期1003-1008,共6页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(40676016；10471039);国家重点基础研究发展规划项目(2003CB415101-03；2004CB418304);中国科学院知识创新工程方向性项目(KZCX3-SW-221);上海市教育委员会E-研究院建设计划项目(NE03004)

摘　　要：在适当的条件下研究了一类具有边界摄动的非线性反应扩散方程奇摄动初始边值问题.首先,借助正规摄动方法,得到了原问题的外部解.其次,利用伸长变量和幂级数展开理论,构造了解的初始层项.然后,利用微分不等式理论,研究了初始边值问题解的渐近性态.最后,利用一些相关的不等式,讨论了原问题解的存在、唯一性及其一致有效的渐近估计.A class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation is considered under suitable conditions. Vastly, by dint of regular perturbation method, the outer solution of the original problem was obtained. Secondly, by using the stretched variable and the expanding theory of power series, the initial layer term of solution was constructed. And then, by using the theory of differential inequalities the asymptotic behavior of solutions for the initial boundary value problems was studied. Finally, using some relational inequalities the existence and tmiqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.

关 键 词：非线性 反应扩散 奇摄动 边界摄动 

分 类 号：O175.29[理学—数学]