带有指数型非线性项的离散泊松方程和热方程

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 773-784.

带有指数型非线性项的离散泊松方程和热方程

李亚峰¹,辛巧¹(),穆春来²

¹ 伊犁师范学院数学与统计分院新疆伊宁 835000
² 重庆大学数学与统计学院重庆 401331

收稿日期:2018-02-28 出版日期:2019-08-26 发布日期:2019-09-11
作者简介:辛巧, E-mail:xinqiaoylsy@163.com
基金资助:
国家自然科学基金(11461075)

The Discrete Possion Equation and the Heat Equation with the Exponential Nonlinear Term

Yafeng Li¹,Qiao Xin¹(),Chunlai Mu²

¹ College of Mathematics and Statistics, Yili Normal University, Xinjiang Yingning 835000
² College of Mathematics and Statistics, Chongqing University, Chongqing 401331

Received:2018-02-28 Online:2019-08-26 Published:2019-09-11
Supported by:
the NSFC(11461075)

摘要/Abstract

摘要：

该文主要利用单调迭代法和比较原理研究了带有指数型非线性项的离散泊松方程和带有指数型非线项的离散热方程解的存在性之间的关系，主要给出了带有指数型非线性项的离散泊松方程解存在时，带有指数型非线项的离散热方程解的渐近稳定性.

关键词: 离散泊松方程, 离散热方程, 图, 比较原理, 爆破

Abstract:

This paper mainly study the relations between the solution of the discrete Poisson equation and the solution of the discrete heat equation with exponential nonlinear term by monotone iterative method and comparison principle. When the solutions of the discrete Poisson equation exist, we discuss the asymptotic stability of the solutions to the discrete heat equation with exponential nonlinear term.

Key words: Discrete Poisson equation, Discrete heat equation, Graph, Comparison principle, Blow-up

中图分类号:

O175.26

李亚峰,辛巧,穆春来. 带有指数型非线性项的离散泊松方程和热方程[J]. 数学物理学报, 2019, 39(4): 773-784.

Yafeng Li,Qiao Xin,Chunlai Mu. The Discrete Possion Equation and the Heat Equation with the Exponential Nonlinear Term[J]. Acta mathematica scientia,Series A, 2019, 39(4): 773-784.

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