Well-posedness of the Cauchy problem for the fractional power dissipative equations
- 作者：Changxing Miao ; Baoquan Yuan ; Bo Zhang
- 关键词：Fractional power dissipative equation ; Cauchy problem ; Well-posedness ; Space– ; time estimates ; Besov spaces
- 刊名：Nonlinear Analysis
- 出版年：2008
- 期刊代码：43_0362546x
- 类别：mt
- 出版时间：1 February 2008
- 卷：68
- 期：3
- 页码：461-484
- 文件大小：435 K
摘要
This paper studies the Cauchy problem for the nonlinear fractional power dissipative equation ut+(−
)αu=F(u) for initial data in the Lebesgue space 
with either r≥rd
nb/(2α−d) or the homogeneous Besov space 
with 56fee030ea6557f7dd845bcec7b94e8" title="Click to view the MathML source">σ=(2α−d)/b−n/p and 1≤p≤∞, where α>0,F(u)=f(u) or Q(D)f(u) with Q(D) being a homogeneous pseudo-differential operator of order d
[0,2α) and f(u) is a function of u which behaves like |u|bu with b>0.
)αu=F(u) for initial data in the Lebesgue space nb/(2α−d) or the homogeneous Besov space [0,2α) and f(u) is a function of u which behaves like |u|bu with b>0.