Self-similar Solutions to a Parabolic System Modelling Chemotaxis
Journal of Differential Equations Volume 184 Issue 2
Page 386-421
published_at 2002-09-20
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| File | |
| Title ( eng ) |
Self-similar Solutions to a Parabolic System Modelling Chemotaxis
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| Creator |
Naito Yūki
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| Source Title |
Journal of Differential Equations
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| Volume | 184 |
| Issue | 2 |
| Start Page | 386 |
| End Page | 421 |
| 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.
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| NDC |
Mathematics [ 410 ]
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| Language |
eng
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| Resource Type | journal article |
| Publisher |
Elsevier Science
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| Date of Issued | 2002-09-20 |
| Rights |
Copyright (c) 2002 Elsevier Science (USA).
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| Publish Type | Author’s Original |
| Access Rights | open access |
| Source Identifier |
[ISSN] 0022-0396
[DOI] 10.1006/jdeq.2001.4146
[NCID] AA00696680
[DOI] http://dx.doi.org/10.1006/jdeq.2001.4146
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