一类非线性微分-积分时滞反应扩散系统奇摄动问题的广义解  

Generalized Solution to the Singular Perturbation Problem for a Class of Nonlinear Differential-Integral Time Delay Reaction Diffusion System

作　　者：韩祥临[1] 汪维刚 莫嘉琪 Xianglin Han;Weigang Wang;Jiaqi Mo(Qiuzhen School of Huzhou Teachers College, Zhejiang Huzhou 313000;Department of Basic, Hefei Preschool Education College, Hefei 230011;School of Mathematics & Statistics, Anhui Normal University, Anhui Wuhu 241003)

机构地区：[1]湖州师范学院求真学院,浙江湖州313000 [2]合肥幼儿师范高等专科学校基础部,合肥230011 [3]安徽师范大学数学与统计学院,安徽芜湖230011

出　　处：《数学物理学报（A辑）》2019年第2期297-306,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(11771005);浙江省自然科学基金(LY13A010005);安徽省高校自然科学研究重点项目(KJ2017A901);安徽省教育科学规划课题(JG10068)~~

摘　　要：该文研究了一类非线性微分-积分时滞广义反应扩散系统奇摄动问题.在适当的条件下,利用奇摄动方法构造了初始-边值问题广义解的渐近展开式.建立了广义解的微分不等式理论,并证明了相应解的存在性及其解的渐近展开式的一致有效性.A class of nonlinear differential-integral system for the singular perturbation generalized reaction diffusion equations with time delay is considered. Under suitable conditions, the asymptotic expansions of generalized solution to the initial boundary problem is obtained by using the singular perturbation method. And the theory of differential inequality for generalized solution is constructed. Corresponding existence and the uniformly validity of the asymptotic expansion for the solution are proved.

关 键 词：反应扩散 奇摄动 非线性系统 

分 类 号：O175.29[理学—数学]