一个初值控制动态问题解的存在性

上海大学学报(自然科学版) ›› 2014, Vol. 20 ›› Issue (6): 741-748.

一个初值控制动态问题解的存在性

童春1,2, 王远弟1

1. 上海大学理学院, 上海200444; 2. 宁波职业技术学院公共教学部, 浙江宁波315800

收稿日期:2013-11-17 出版日期:2014-12-23 发布日期:2014-12-23
作者简介:王远弟(1965—), 男, 教授, 博士生导师, 博士, 研究方向为偏微分方程. E-mail: ydwang@shu.edu.cn
基金资助:
上海高校一流学科资助项目

Existence of Solutions for an Initial Control Problem with Dynamic Boundary Conditions

TONG Chun1,2, WANG Yuan-di1

1. College of Sciences, Shanghai University, Shanghai 200444, China;2. Department of Public Teaching, Ningbo Polytechnic, Ningbo 315800, Zhejiang, China

Received:2013-11-17 Online:2014-12-23 Published:2014-12-23

摘要/Abstract

摘要： 讨论了一个抛物型偏微分方程动态边值的初值控制问题. 在一定条件下得出了上下解的有序性, 并由此引入迭代序列讨论了整体解的存在性以及计算办法, 并给出了问题具有无穷多解的算例.

关键词: 边值问题, 非局部, 极值原理, 控制问题, 抛物型方程, 上下解

Abstract: An initial control problem with dynamic boundary conditions is investigated by using a method of maximal principle. The comparison principle and existence of solutions for the control problem under some assumptions are proved. Some examples with multiple solutions and unique solution are gived.

Key words: boundary value problem;upper-lower solutions, control problem, maximal principle, nonlocal, parabolic equation

中图分类号:

O 175.2

童春1, 2, 王远弟1. 一个初值控制动态问题解的存在性[J]. 上海大学学报(自然科学版), 2014, 20(6): 741-748.

TONG Chun-1, 2 , WANG Yuan-Di-1. Existence of Solutions for an Initial Control Problem with Dynamic Boundary Conditions[J]. Journal of Shanghai University（Natural Science Edition）, 2014, 20(6): 741-748.

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