自相似分形上的非线性抛物方程(英文)  

NON-LINEAR PARABOLIC EQUATIONS ON SELF-SIMILAR FRACTAL SETS

作　　者：贺振亚[1] 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》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)

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.

关 键 词：分形 抛物方程 比较原理 上下解 

分 类 号：O175.29[理学—数学]