分数阶反应扩散方程解的存在性与惟一性的单调迭代方法

J4 ›› 2011, Vol. 46 ›› Issue (2): 9-14.

分数阶反应扩散方程解的存在性与惟一性的单调迭代方法

张翔,黄淑祥

山东大学数学学院, 山东济南 250100

收稿日期:2010-01-26 出版日期:2011-02-16 发布日期:2011-03-30

Monotone iterative technique, existence and uniqueness results for the nonlinear fractional reaction-diffusion equation

ZHANG Xiang, HUANG Shu-xiang

School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2010-01-26 Online:2011-02-16 Published:2011-03-30
About author:ZHANG Xiang(1985- ), Male, Master, his research mainly focuses on partial differential equations. Email: xiangzhang@mail.sdu.edu.cn

摘要/Abstract

摘要：

利用单调迭代方法研究非线性分数阶反应扩散方程初边值问题解的存在与惟一性。另外把上下解引用到分数阶反应扩散方程,且在文末给出两个例子验证了定理。

关键词: 分数阶反应扩散方程; 单调迭代技术; 上下解; 存在性与惟一性; Caputo 分数阶导数

Abstract:

Existence and uniqueness for the initial-boundary value problem of the nonlinear fractional reaction-diffusion equation are considered by the monotone iterative method. The upper and lower solutions are developed for the fractional reaction-diffusion. Finally, two examples are given to illustrate the results.

Key words: nonlinear fractional reaction-diffusion equation; monotone iterative technique; upper and lower solutions; existence and uniqueness; Caputo fractional derivative

张翔,黄淑祥. 分数阶反应扩散方程解的存在性与惟一性的单调迭代方法[J]. J4, 2011, 46(2): 9-14.

ZHANG Xiang, HUANG Shu-xiang. Monotone iterative technique, existence and uniqueness results for the nonlinear fractional reaction-diffusion equation[J]. J4, 2011, 46(2): 9-14.

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