Large time convergence for a chemotaxis model with degenerate local sensing and consumption

Philippe LAURENCOT

doi:10.4134/BKMS.b230173

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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

Large time convergence for a chemotaxis model with degenerate local sensing and consumption

Philippe LAURENCOT

Universit\'e Savoie Mont Blanc, CNRS

Abstract

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Abstract

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