Long term spatial homogeneity for a chemotaxis model with local sensing and consumption

Global weak solutions to a chemotaxis model with local sensing and consumption are shown to converge to spatially homogeneous steady states in the large time limit, when the motility is assumed to be positive and $C^1$-smooth on $[0,\infty)$. The result is valid in arbitrary space dimension $n \geq1$ and extends a previous result which only deals with space dimensions $n \in {\lbrace 1,2,3 \rbrace}$.

Keywords

convergence, Liapunov functional, chemotaxis-consumption model, local sensing

2010 Mathematics Subject Classification

35B40, 35K51, 35Q92, 37L45

Full Text (PDF format)

Received 1 March 2023

Received revised 30 June 2023

Accepted 2 July 2023

Published 22 September 2023