このエントリーをはてなブックマークに追加
ID 21529
file
creator
Naito, Yūki
NDC
Mathematics
abstract
We study the forward self-similar solutions to a parabolic system modeling chemotaxis ut=∇·(∇u-u∇v), rvt=∇v+u in the whole space R2, where τ is a positive constant. Using the Liouville-type result and the method of moving planes, it is proved that self-similar solutions (u,v) must be radially symmetric about the origin. Then the structure of the set of self-similar solutions is investigated. As a consequence, it is shown that there exists a threshold in ∫R2u for the existence of self-similar solutions. In particular, for 0<r≤1/2, there exists a self-similar solution (u,v) if and only if ∫R2u<8.
journal title
Journal of Differential Equations
volume
Volume 184
issue
Issue 2
start page
386
end page
421
date of issued
2002-09-20
publisher
Elsevier Science
issn
0022-0396
ncid
publisher doi
language
eng
nii type
Journal Article
HU type
Journal Articles
DCMI type
text
format
application/pdf
text version
author
rights
Copyright (c) 2002 Elsevier Science (USA).
relation url
department
Graduate School of Science