带有指数型非线性项的离散泊松方程和热方程  

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

作　　者：李亚峰 辛巧[1] 穆春来[2] Li Yafeng;Xin Qiao;Mu Chunlai(College of Mathematics and Statistics, Yili Normal University,Xinjiang Yingning 835000;College of Mathematics and Statistics, Chongqing University,Chongqing 401331)

机构地区：[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

出　　处：《数学物理学报（A辑）》2019年第4期773-784,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11461075)~~

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.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.

关 键 词：离散泊松方程 离散热方程 图 比较原理 爆破 

分 类 号：O175.26[理学—数学]