拟线性双重退化抛物方程的自相似解  

The Self-similar Solutions for a Quasilinear Doubly Degenerate Parabolic Equation

作　　者：詹华税[1] 

机构地区：[1]集美大学理学院,厦门361021

出　　处：《工程数学学报》2010年第6期1030-1034,共5页Chinese Journal of Engineering Mathematics

基　　金：福建省自然科学基金(2009J01009);集美大学科学基金~~

摘　　要：本文研究一类带有非线性梯度项的拟线性双重退化抛物方程的自相似奇性解的存在性及其分类。该类方程包含著名的Hamilton-Jacobi方程,牛顿流和非牛顿流渗流方程。本文通过标准的皮卡迭代方法,得到了该方程的自相似奇性解存在的充分条件,同时给出了相应奇性解的分类。This paper considers a quasilinear doubly degenerate parabolic equation with a nonlinear gradient term,we study the existence of its self-similar singular solutions and consider the correspond-ing classification.The equation includes the well-known Hamililton-Jacobi equation,the Newtonian filtration equation and the non-Newtonian filtration equation as its special forms.By the standard Picard iteration method,a suficient condition about the existence of singular self-similar solutions for the equation is obtained,and a classification for these singular self-similar solutions is given.

关 键 词：拟线性双重退化抛物方程 自非线性梯度项 自相似解 奇性解 

分 类 号：O175.27[理学—数学]