Nondegeneracy of blow-up points for the parabolic Keller–Segel system
Nondegeneracy of blow-up points for the parabolic Keller–Segel system
复制标题
DOI：
10.1016/j.anihpc.2013.07.007
复制
发表时间：
2014-07
影响因子：
1.9
通讯作者：
N. Mizoguchi;P. Souplet
中科院分区：
文献类型：
--
作者：
N. Mizoguchi;P. Souplet
r vt= v-λv+ u，在Ω×（0，T）中，在RN的域Ω中，N 1，其中m、r> 0、λ 0是常数且T> 0。当Ω= RN时，我们在边界上施加Neumann边界条件。在适当的假设下，我们证明了爆破点的局部非退化性。这似乎是新的，即使是经典的Keller-Segel系统（m= 1）。较低的整体爆破估计也得到了。在奇异情况0< m< 1下，作为先决条件，建立了局部存在性和正则性。All rights reserved.
Γ vt= v− λv+ u in Ω×(0, T), in a domain Ω of RN with N⩾ 1, where m, Γ> 0, λ⩾ 0 are constants and T> 0. When Ω= RN, we impose the Neumann boundary conditions on the boundary. Under suitable assumptions, we prove the local nondegeneracy of blow-up points. This seems new even for the classical Keller–Segel system (m= 1). Lower global blow-up estimates are also obtained. In the singular case 0< m< 1, as a prerequisite, local existence and regularity properties are established.© 2013 Elsevier Masson SAS. All rights reserved.