Xuhuan Zhou, Weiliang Xiao, Jiecheng Chen
Abstract:
In this article, we consider the evolution model
We show that when
,
,
, the equation
has a unique local in time solution for any initial data in
.
Moreover, in the critical case
,
the solution exists in
,
,
,
.
Submitted April 10, 2014. Published September 23, 2014.
Math Subject Classifications: 35K55, 35K65, 76S05.
Key Words: Fractional porous medium equation; mean field equation;
local solution; Besov space.
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Xuhuan Zhou Department of Mathematics, Zhejiang University 310027 Hangzhou, China email: zhouxuhuan@163.com | |
Weiliang Xiao Department of Mathematics, Zhejiang University 310027 Hangzhou, China email: xwltc123@163.com | |
Jiecheng Chen Department of Mathematics, Zhejiang Normal University 321004 Jinhua, China email: jcchen@zjnu.edu.cn |
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