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

Philippe Laurencot
대한수학회 (The Korean Mathematical Society)|2024.03|대한수학회보 (Bulletin of the KMS)|제61권 제2호|pp. 479-488|DOI 10.4134/BKMS.b230173

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키워드

Convergencechemotaxis-consumption modellocal sensing
주제분류수학

초록

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.

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.

참고문헌 (26)

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