A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint

Fujie, Kentarou; Senba, Takasi

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 275-282

Abstract

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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 π ) 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 π 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.

How to cite

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Fujie, Kentarou, and Senba, Takasi. "A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 275-282. <http://eudml.org/doc/294906>.

@inProceedings{Fujie2017,
abstract = {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.},
author = {Fujie, Kentarou, Senba, Takasi},
booktitle = {Proceedings of Equadiff 14},
keywords = {Chemotaxis; global existence; Lyapunov functional; Adams’ inequality},
location = {Bratislava},
pages = {275-282},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint},
url = {http://eudml.org/doc/294906},
year = {2017},
}

TY - CLSWK
AU - Fujie, Kentarou
AU - Senba, Takasi
TI - A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 275
EP - 282
AB - 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.
KW - Chemotaxis; global existence; Lyapunov functional; Adams’ inequality
UR - http://eudml.org/doc/294906
ER -

References

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