Existence of self-similar solutions to a parabolic system modelling chemotaxis

被引：0
作者：
Naomi Muramoto
Yūki Naito
Kiyoshi Yoshida
机构：
[1] Hiroshima University,Department of Mathematics, Faculty of Science
[2] Kobe University,Department of Applied Mathematics, Faculty of Engineering
[3] Hiroshima University,Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences
来源：
Japan Journal of Industrial and Applied Mathematics | 2000年 / 17卷
关键词：
self-similar solution; chemotaxis; elliptic equation; global branch;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We investigate a semilinear elliptic equation[graphic not available: see fulltext] with a parameter λ > 0 and a constant 0 < ε < 2, and obtain a structure of the pair (λ, υ) of a parameter and a solution which decays at infinity. This equation arises in the study of self-similar solutions for the Keller-Segel system. Our main results are as follows: (i) There exists a λ* > 0 such that if 0 < λ < λ*, (SE) has two distinct solutionsυλ and guλ satisfyingυλ < guλ, and that if λ > λ*, (SE) has no solution, (ii) If λ = λ* and 0 < ε < 1, (SE) has the unique solution υ*; (iii) The solutionsυλ and υλ are connected through υ*.
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页码：427 / 451
页数：24
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