| Title:
|
A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint (English) |
| Author:
|
Fujie, Kentarou |
| Author:
|
Senba, Takasi |
| Language:
|
English |
| Journal:
|
Proceedings of Equadiff 14 |
| Volume:
|
Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017 |
| Issue:
|
2017 |
| Year:
|
|
| Pages:
|
275-282 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider initial boundary problems of a two-chemical substances chemotaxis system. In the four-dimensional setting, it was shown that solutions exist globally in time and remain bounded if the total mass is less than $(8\pi)^2$, whereas the solution emanating from some initial data of large magnitude may blows up. This result can be regarded as a generalization of the well-known $8\pi$ problem in the Keller–Segel system to higher dimensions. We will compare mathematical structures of the Keller–Segel system and our system and discuss the difference. (English) |
| Keyword:
|
Chemotaxis; global existence; Lyapunov functional; Adams’ inequality |
| MSC:
|
35B45 |
| MSC:
|
35K45 |
| MSC:
|
35Q92 |
| MSC:
|
92C17 |
| . |
| Date available:
|
2019-09-27T08:11:05Z |
| Last updated:
|
2019-09-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703047 |
| . |
| Reference:
|
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