一类弱非线性奇摄动微分差分方程的阶梯状空间对照结构  

Step-Type Contrast Structure for a Class of Weak Nonlinear Singularly Perturbed Differential-Difference Equation

作　　者：王爱峰[1] WANG Aifeng(School of Mathematical Science, Huai yin Normal University, Huai ＇an 223300, Jiangsu Province, Chin)

机构地区：[1]淮阴师范学院数学科学学院,江苏淮安223300

出　　处：《吉林大学学报（理学版）》2018年第3期508-514,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11501236)

摘　　要：利用边界函数法和分步法构造一类弱非线性奇摄动微分差分方程的阶梯状空间对照结构的渐近解,得到了产生对照结构的时刻t=t*,并借助缝接法证明内部层光滑解的存在性及所构造形式渐近解的一致有效性.Using the methods of boundary function and fractional steps,the author constructed the asymptotic solution of step-type contrast structure for a class of weak nonlinear singularly perturbed differential-difference equation,and obtained the time t=t＊to produce a contrast structure.By means of sewing method,the author proved the existence of the smooth solution of interior layer and the uniform validity of the asymptotic solution of the form.

关 键 词：微分差分方程 渐近展开 边界函数 对照结构 

分 类 号：O175[理学—数学]