Local well-posedness and finite time blow-up of solutions to an attraction–repulsion chemotaxis system in higher dimensions

Tatsuya Hosono; Takayoshi Ogawa

doi:10.1016/j.jmaa.2022.126009

Local well-posedness and finite time blow-up of solutions to an attraction–repulsion chemotaxis system in higher dimensions

Tatsuya Hosono, Takayoshi Ogawa

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the Cauchy problem for an attraction–repulsion chemotaxis system in Rⁿ with the chemotactic coefficients of the attractant β₁ and the repellent β₂. In particular, these coefficients are important role in the global existence and blow up of the solutions. In this paper, we show the local well-posedness of solutions in the critical spaces L^n/2(Rⁿ) and the finite time blow-up of the solution under the condition β₁>β₂ in higher dimensional spaces.

Original language	English
Article number	126009
Journal	Journal of Mathematical Analysis and Applications
Volume	510
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2022.126009
Publication status	Published - 2022 Jun 1

Keywords

Attraction–repulsion chemotaxis system
Blow-up
Cauchy problem
Well-posedness

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2022.126009

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title = "Local well-posedness and finite time blow-up of solutions to an attraction–repulsion chemotaxis system in higher dimensions",

abstract = "We consider the Cauchy problem for an attraction–repulsion chemotaxis system in Rn with the chemotactic coefficients of the attractant β1 and the repellent β2. In particular, these coefficients are important role in the global existence and blow up of the solutions. In this paper, we show the local well-posedness of solutions in the critical spaces Ln/2(Rn) and the finite time blow-up of the solution under the condition β1>β2 in higher dimensional spaces.",

keywords = "Attraction–repulsion chemotaxis system, Blow-up, Cauchy problem, Well-posedness",

author = "Tatsuya Hosono and Takayoshi Ogawa",

note = "Funding Information: The authors are grateful to the referee for careful reading and helpful suggestions. The work of T. Hosono is supported by JST SPRING, Grant Number JPMJSP2114 . The work of T. Ogawa is partially supported by JSPS Grant-in-Aid for Scientific Research (S) # 19H05597 and Challenging Research (Pioneering) # 20K20284 . Publisher Copyright: {\textcopyright} 2022 The Authors",

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doi = "10.1016/j.jmaa.2022.126009",

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AU - Hosono, Tatsuya

AU - Ogawa, Takayoshi

N1 - Funding Information: The authors are grateful to the referee for careful reading and helpful suggestions. The work of T. Hosono is supported by JST SPRING, Grant Number JPMJSP2114 . The work of T. Ogawa is partially supported by JSPS Grant-in-Aid for Scientific Research (S) # 19H05597 and Challenging Research (Pioneering) # 20K20284 . Publisher Copyright: © 2022 The Authors

PY - 2022/6/1

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N2 - We consider the Cauchy problem for an attraction–repulsion chemotaxis system in Rn with the chemotactic coefficients of the attractant β1 and the repellent β2. In particular, these coefficients are important role in the global existence and blow up of the solutions. In this paper, we show the local well-posedness of solutions in the critical spaces Ln/2(Rn) and the finite time blow-up of the solution under the condition β1>β2 in higher dimensional spaces.

AB - We consider the Cauchy problem for an attraction–repulsion chemotaxis system in Rn with the chemotactic coefficients of the attractant β1 and the repellent β2. In particular, these coefficients are important role in the global existence and blow up of the solutions. In this paper, we show the local well-posedness of solutions in the critical spaces Ln/2(Rn) and the finite time blow-up of the solution under the condition β1>β2 in higher dimensional spaces.

KW - Attraction–repulsion chemotaxis system

KW - Blow-up

KW - Cauchy problem

KW - Well-posedness

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VL - 510

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ER -

Local well-posedness and finite time blow-up of solutions to an attraction–repulsion chemotaxis system in higher dimensions

Abstract

Keywords

ASJC Scopus subject areas

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