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Self-Similar Solutions to a Parabolic System Modeling Chemotaxis

✍ Scribed by Yūki Naito; Takashi Suzuki; Kiyoshi Yoshida

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
291 KB
Volume
184
Category
Article
ISSN
0022-0396

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✦ Synopsis

We study the forward self-similar solutions to a parabolic system modeling chemotaxis

in the whole space R 2 ; where t is a positive constant. Using the Liouville-type result and the method of moving planes, it is proved that self-similar solutions ðu; vÞ must be radially symmetric about the origin. Then the structure of the set of selfsimilar solutions is investigated. As a consequence, it is shown that there exists a threshold in R R 2 u for the existence of self-similar solutions. In particular, for 05t 41=2; there exists a self-similar solution ðu; vÞ if and only if R R 2 u58p: # 2002 Elsevier Science (USA)

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