THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION  

作　　者：王爱峰 倪明康 

机构地区：[1]Department of Mathematics,East China Normal University [2]School of Mathematical Science,Huaiyin Normal University [3]Division of Computational Science,E-Institute of Shanghai Universities at SJTU

出　　处：《Acta Mathematica Scientia》2012年第2期695-709,共15页数学物理学报（B辑英文版）

基　　金：Supported by the National Natural Science Funds (11071075);the Natural Science Foundation of Shanghai(10ZR1409200);the National Laboratory of Biomacromolecules,Institute of Biophysics,Chinese Academy of Sciences;the E-Institutes of Shanghai Municipal Education Commissions(E03004)

摘　　要：In this article, the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered. Using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and point out that the boundary layer at t = 0 has a great influence upon the interior layer at t = a. At the same time, on the basis of differential inequality techniques, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of our result. The result of this article is new and it complements the previously known ones.In this article, the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered. Using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and point out that the boundary layer at t = 0 has a great influence upon the interior layer at t = a. At the same time, on the basis of differential inequality techniques, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of our result. The result of this article is new and it complements the previously known ones.

关 键 词：Differential-difference equation interior layer asymptotic expansion bound-ary function 

分 类 号：O175.7[理学—数学] O175.25[理学—基础数学]