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高校应用数学学报
高校应用数学学报  2016, Vol. 31 Issue (3): 307-315    
    
一类奇摄动半线性时滞抛物型偏微分方程的渐近解
包立平
杭州电子科技大学 理学院, 浙江杭州 310018
The asymptotic solution of a class of singular perturbed semi-linear delayed parabolic partial differential equation
BAO Li-ping
School of Science , Hangzhou Dianzi University, Hangzhou 310018, China
 全文: PDF 
摘要： 文中讨论了一类奇摄动时滞抛物型偏微分方程的初边值问题, 得到了其形式渐近展开, 证明了奇摄动半线性时滞偏微分方程的极大值原理, 从而得到了最大值估计及相应的Schuader估计. 在此基础上, 得到了柱状区域上解的存在唯一性和渐近解的一致有效性.
关键词： 奇摄动;  半线性;  时滞抛物型方程;  渐近展开;  Schuader估计;  最大值原理;  余项估计    
Abstract: In this paper, a class of initial boundary problem of the singular perturbed semi-linear delayed parabolic partial differential equation is discussed. The formal asymptotic expansion of the problem is obtained. The maximum principle of the singular perturbed delayed semi-linear parabolic partial differential equations is proved. Then, the maximum-norm estimation and Schauder estimation for this problem are obtained. By the maximum-norm estimation and Schauder estimation for this problem, the existence and uniqueness of the solution of the problem on the columnar zone is proved, and the uniformly valid estimation of the asymptotic expansion is gained.
Key words: singular perturbation    semi-linear    delay parabolic differential equation    asymptotic expansion    Schauder estimation    maximum-norm estimation    estimation of the remainder
收稿日期: 2015-11-25 出版日期: 2018-05-16
CLC:  O175.12  
基金资助: 国家自然科学基金(51175134)
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引用本文:

包立平. 一类奇摄动半线性时滞抛物型偏微分方程的渐近解[J]. 高校应用数学学报, 2016, 31(3): 307-315.

BAO Li-ping. The asymptotic solution of a class of singular perturbed semi-linear delayed parabolic partial differential equation. Applied Mathematics A Journal of Chinese Universities, 2016, 31(3): 307-315.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2016/V31/I3/307

[1] 包立平. 一类具有不连续源的奇摄动半线性微分方程组边值问题[J]. 高校应用数学学报, 2017, 32(4): 413-422.