摘要
本文研究了具有非线性非局部边界条件的一类退化型多孔介质方程.利用比较原理和上下解的方法,获得了方程的解是否在有限时刻爆破或整体存在的准则,这些结果表明,权重函数g(x,y)及指数l的大小对于问题解的爆破与否起着关键的作用.最后研究了爆破解的爆破率.
This paper studies a degenerate nonlinear porous medium equation ut ： Aum ＋aup fa uqdx with nonlinear and nonlocal boundary condition uloЭΩ（0,∞） ： fΩ g（x,y）ul（y,t）dy.With the help of the comparison principle and super, sub-solution methods, some criteria on thisproblem which determine whether the solutions blow up in a finite time or the solutions exist forall time are given. These results show that the global existence and blow-up results depend on theweight function g（x, y） and the size of l. Finally, the blow-up rate of the blow-up solutions is given.
出处
《数学杂志》
CSCD
北大核心
2014年第6期1091-1100,共10页
Journal of Mathematics
基金
Supported by National Natural Science Foundation of China(11461076)
Universities and colleges research foundation of Guangxi(ZD2014106)
关键词
多孔介质方程
非线性非局部边界条件
整体存在
爆破
爆破率
porous medium equation
nonlinear nonlocal boundary condition
global exis-tence
blow-up： b/ow-lln rnto
