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

数学物理学报 ›› 2019, Vol. 39 ›› Issue (2): 297-306.

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

韩祥临¹(),汪维刚²,莫嘉琪³

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

收稿日期:2017-10-31 出版日期:2019-04-26 发布日期:2019-05-05
作者简介:韩祥临, E-mail: xlhan@zjhu.edu.cn
基金资助:
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)

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

Xianglin Han¹(),Weigang Wang²,Jiaqi Mo³

¹ Qiuzhen School of Huzhou Teachers College, Zhejiang Huzhou 313000
² Department of Basic, Hefei Preschool Education College, Hefei 230011
³ School of Mathematics & Statistics, Anhui Normal University, Anhui Wuhu 241003

Received:2017-10-31 Online:2019-04-26 Published:2019-05-05
Supported by:
the NSFC(11771005);the Natural Science Foundation of Zhejiang Province(LY13A010005);the Natural Science Foundation of the Education Department of Anhui Province(KJ2017A901);the Education Science Programming Foundation of Anhui Province(JG10068)

摘要/Abstract

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.

关键词: 反应扩散, 奇摄动, 非线性系统

Abstract:

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.

Key words: Reaction diffusion, Singular perturbation, Nonlinear system

中图分类号:

O175.29

韩祥临,汪维刚,莫嘉琪. 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[J]. 数学物理学报, 2019, 39(2): 297-306.

Xianglin Han,Weigang Wang,Jiaqi Mo. Generalized Solution to the Singular Perturbation Problem for a Class of Nonlinear Differential-Integral Time Delay Reaction Diffusion System[J]. Acta mathematica scientia,Series A, 2019, 39(2): 297-306.

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