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THE NONLINEAR NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH A BOUNDARY PERTURBATION
作者姓名:Jingsun  Yao  Jiaqi  Mo
作者单位:Department of Mathematics Anhui Normal University, Wuhu, 241000 P. R. China
基金项目:国家自然科学基金 , 国家重点基础研究发展计划(973计划) , 中国科学院资助项目 , 浙江省自然科学基金
摘    要:The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.

关 键 词:奇异扰动  反向扩散方程  边界扰动  单一性  匹配条件
收稿时间:2003-09-30
修稿时间:2004-11-02

The nonlinear nonlocal singularly perturbed problems for reaction diffusion equations with a boundary perturbation
Jingsun Yao Jiaqi Mo.THE NONLINEAR NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH A BOUNDARY PERTURBATION[J].Analysis in Theory and Applications,2005,21(3):242-248.
Authors:Jingsun Yao  Jiaqi Mo
Institution:(1) Department of Mathematics, Anhui Normal University, 241000 Wuhu, P. R. China
Abstract:The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Keywords:nonlinear  reaction diffusion  singular perturbation  BOUNDARY PERTURBATION  REACTION DIFFUSION EQUATIONS  PROBLEMS  SINGULARLY PERTURBED  NONLOCAL  existence  uniqueness of solution  valid  the asymptotic behavior  estimation  differential inequalities  composing  expansion method  expanding  theory  power series  initial layer  variable  original  boundary value problems
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