Electron. J. Differential Equations, Vol. 2021 (2021), No. 71, pp. 1-10.

Existence of bounded global solutions for fully parabolic attraction-repulsion chemotaxis systems with signal-dependent sensitivities and without logistic source

Yutaro Chiyo, Masaaki Mizukami, Tomomi Yokota

Abstract:
This article concerns the parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities

under homogeneous Neumann boundary conditions and initial conditions, where $\Omega \subset \mathbb{R}^n$ $(n \ge 2)$ is a bounded domain with smooth boundary, $\chi, \xi$ are functions satisfying certain conditions. Existence of bounded global classical solutions to the system with logistic source and logistic damping have been obtained in [1]. This article establishes the existence of global bounded classical solutions with logistic damping.

Submitted April 8, 2021. Published September 10, 2021.
Math Subject Classifications: 35A01, 35Q92, 92C17.
Key Words: Chemotaxis; attraction-repulsion; existence; boundedness.
DOI: https://doi.org/10.58997/ejde.2021.71

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Yutaro Chiyo
Department of Mathematics
Tokyo University of Science
1-3, Kagurazaka, Shinjuku-ku
Tokyo 162-8601, Japan
email: ycnewssz@gmail.com
Masaaki Mizukami
Department of Mathematics
Faculty of Education
Kyoto University of Education
1, Fujinomori, Fukakusa, Fushimi-ku
Kyoto 612-8522, Japan
email: masaaki.mizukami.math@gmail.com
Tomomi Yokota
Department of Mathematics
Tokyo University of Science
1-3, Kagurazaka, Shinjuku-ku
Tokyo 162-8601, Japan
email: yokota@rs.tus.ac.jp

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