On a hyperbolic-parabolic chemotaxis system

Hongyun Peng; Kun Zhao; Hongyun Peng; Kun Zhao

doi:10.3934/mbe.2023337

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 7802-7827. doi: 10.3934/mbe.2023337

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On a hyperbolic-parabolic chemotaxis system

Hongyun Peng ^{1
,
,},
Kun Zhao ²

1.
School of Mathematics and Statistics, GuangDong University of Technology, Guangzhou, 510006, China
2.
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA

Received: 01 October 2022 Revised: 17 January 2023 Accepted: 06 February 2023 Published: 21 February 2023

Stability of steady state solutions associated with initial and boundary value problems of a coupled fluid-reaction-diffusion system in one space dimension is analyzed. It is shown that under Dirichlet-Dirichlet type boundary conditions, non-trivial steady state solutions exist and are locally stable when the system parameters satisfy certain constraints.
- hyperbolic-parabolic system,
- chemotaxis,
- initial-boundary value problem,
- classical solution,
- global existence,
- long-time behavior
Citation: Hongyun Peng, Kun Zhao. On a hyperbolic-parabolic chemotaxis system[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 7802-7827. doi: 10.3934/mbe.2023337

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Abstract

Stability of steady state solutions associated with initial and boundary value problems of a coupled fluid-reaction-diffusion system in one space dimension is analyzed. It is shown that under Dirichlet-Dirichlet type boundary conditions, non-trivial steady state solutions exist and are locally stable when the system parameters satisfy certain constraints.

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