Global existence and uniform boundedness in a chemotaxis model with signal-dependent motility

By Jie Jiang, Philippe Laurencçot. 2021

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Abstract Global existence is established for classical solutions to a chemotaxis model with signal-dependent motility for a general class of motility functions γ which may in particular decay in an arbitrary way at infinity. Assuming further that γ is non-increasing and decays sufficiently slowly at infinity, in the sense that γ ( s ) ∼ s − k as s → ∞ for some k ∈ ( 0 , N / ( N − 2 ) + ) , it is also shown that global solutions are uniformly bounded with respect to time. The admissible decay of γ at infinity here is higher than in previous works.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/2c800faf643e0b511f54979d7d0aaed09be85eaa

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Citations in the corpus

Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities (2022, background): “also [19], [21], [38], [45], [28], [29] and [30] for corresponding studies on some close relatives), but also on large time asymptotics, and especially on the identification of situations in which either stabilization toward equilibria can be observed, or, alternatively, infinite-time blow-up occurs”
A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion (2022, unknown): “Besides basic results on global solvability (see [1], [14], [11], [10], [4], [15], [35], [34] and also [40]), several studies also include findings on asymptotic behavior, mainly identifying diffusion-dominated constellations in which solutions to either (1.”
Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities (2022, background): “1) ([9], [1], [8], [28], [2], [3]), as well as some close variants ([12], [6], [11], [14], [30], [37], [22], [23]); beyond this, results on spatially structured large time behavior, and even on the occurrence of infinite-time blow-up ([7], [9], [13], [1], [4]), provide conclusive evidence for signif”