摘要
本文研究了分形区域上的一类半线性抛物方程.对于分形上恰当定义的拉普拉斯算子,建立了抛物方程的比较原理.利用上下解方法,我们得到了在一定条件下半线性抛物方程正解的存在性和唯一性.
This article investigates non-linear parabolic equations on fractal sets. With an appropriately defined Laplacian, we construct comparison principle for a class of parabolic equations on fractal sets. By means of the upper-lower-solution method, we obtain the existence and uniqueness of positive solutions of a class of semi-linear parabolic equations with certain boundary conditions.
出处
《数学杂志》
CSCD
北大核心
2010年第1期1-9,共9页
Journal of Mathematics
基金
Supported by by the National Natural Science Foundation of China(70871094)
关键词
分形
抛物方程
比较原理
上下解
fractal
parabolic equation
comparison principle
upper-lower solution
