Bull. Korean Math. Soc. 2024; 61(2): 479-488
Online first article March 19, 2024 Printed March 31, 2024
https://doi.org/10.4134/BKMS.b230173
Copyright © The Korean Mathematical Society.
Philippe LAURENCOT
Universit\'e Savoie Mont Blanc, CNRS
Convergence to a steady state in the long term limit is established for global weak solutions to a chemotaxis model with degenerate local sensing and consumption, when the motility function is $C^1$-smooth on $[0,\infty)$, vanishes at zero, and is positive on $(0,\infty)$. A condition excluding that the large time limit is spatially homogeneous is also provided. These results extend previous ones derived for motility functions vanishing algebraically at zero and rely on a completely different approach.
Keywords: Convergence, chemotaxis-consumption model, local sensing
MSC numbers: Primary 35B40, 35K65, 35K51, 35Q92
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