初值函数符号对一类非线性偏微分方程解的影响  

The Influence of the Sign of the Initial Value on the Solution of a Non-Linear Partial Differential Equation

作　　者：王柯[1] 张辉[1] 周振娜[1] 

机构地区：[1]北京师范大学数学科学学院,北京100875

出　　处：《数学的实践与认识》2013年第16期203-206,共4页Mathematics in Practice and Theory

基　　金：中央高校基本科研业务费专项资金

摘　　要：研究了一类非线性偏微分方程的极值原理,发现不含有线性项的方程的极值原理总是成立的,与初值函数的符号无关,而含有线性项的方程的极值原理受初值函数符号的影响,在初值函数非负时可以证明,而初值函数非正的时候则不成立,并利用数值解进行了验证.Here we investigate the maximum principle of a non-linear partial differential equation. We found that the maximum principle of the equation without the linear term always holds, with no relevance to the sign of the initial function. Meanwhile the maximum principle of the equation with the linear term is influenced by the sign of the initial function. This can be verified when the initial function is non-negative and cannot be verified when the initial function is non-positive. All these have been verified through numerical solution.

关 键 词：非线性偏微分方程 极值原理 数值解 

分 类 号：O175.29[理学—数学]