TY - JOUR

T1 - Global existence and infinite time blow-up of classical solutions to chemotaxis systems of local sensing in higher dimensions

AU - Fujie, Kentaro

AU - Senba, Takasi

N1 - Funding Information:
The authors thank the referee for valuable comments. K. Fujie is supported by Japan Society for the Promotion of Science (Grant-in-Aid for Early-Career Scientists; No. 19K14576 ). T. Senba is supported by Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research(C); No. 18K03386 )
Publisher Copyright:
© 2022 Elsevier Ltd

PY - 2022/9

Y1 - 2022/9

N2 - This paper deals with the fully parabolic chemotaxis system of local sensing in higher dimensions. Despite the striking similarity between this system and the Keller–Segel system, we prove the absence of finite-time blow-up phenomenon in this system even in the supercritical case. It means that for any regular initial data, independently of the magnitude of mass, the classical solution exists globally in time in the higher dimensional setting. Moreover, for the exponential decaying motility case, it is established that solutions may blow up at infinite time for any magnitude of mass. In order to prove our theorem, we deal with some auxiliary identity as an evolution equation with a time dependent operator. In view of this new perspective, the direct consequence of the abstract theory is rich enough to establish global existence of the system.

AB - This paper deals with the fully parabolic chemotaxis system of local sensing in higher dimensions. Despite the striking similarity between this system and the Keller–Segel system, we prove the absence of finite-time blow-up phenomenon in this system even in the supercritical case. It means that for any regular initial data, independently of the magnitude of mass, the classical solution exists globally in time in the higher dimensional setting. Moreover, for the exponential decaying motility case, it is established that solutions may blow up at infinite time for any magnitude of mass. In order to prove our theorem, we deal with some auxiliary identity as an evolution equation with a time dependent operator. In view of this new perspective, the direct consequence of the abstract theory is rich enough to establish global existence of the system.

KW - Chemotaxis

KW - Global existence

KW - Keller–Segel system

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U2 - 10.1016/j.na.2022.112987

DO - 10.1016/j.na.2022.112987

M3 - Article

AN - SCOPUS:85130549852

SN - 0362-546X

VL - 222

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 112987

ER -