Large time behavior of solutions for density-suppressed motility system in higher dimensions

By Zheng-rong Liu, Jiao Xu. Journal of Mathematical Analysis and Applications, 2019

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Abstract In this paper, we study the asymptotic stability of the following density-suppressed motility system ( ⁎ ) { u t = Δ ( γ ( v ) u ) + μ u ( 1 − u ) , x ∈ Ω , t > 0 , v t = Δ v + u − v , x ∈ Ω , t > 0 , in a bounded domain with smooth boundary, where the motility function γ ( v ) and μ are positive. Under the conditions that the motility function γ ( v ) has the lower-upper bounded and that μ is large enough, we derive that system (⁎) possesses a unique global solution in three-dimensional space. Moreover, we show that if the global classical solution exists of system (⁎) in any dimensional space, then the solution will converge to the equilibrium ( 1 , 1 ) exponentially as t → + ∞ when μ > K 0 16 with K 0 = max 0 ≤ v ≤ ∞ ⁡ | γ ′ ( v ) | 2 γ ( v ) .

Subfields: Computational Theory and Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/880230f6f0a48aefd5ee7e1cd2503902f4e7114a

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Citations in the corpus

A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion (2022, background): “2) or certain closely related variants stabilize toward homogeneous equilibria ([13], [34], [8], [15], [26], [28], [29], [27], [42]).”
Logistic damping effect in chemotaxis models with density-suppressed motility (2021, result): “Later, similar results were extended to higher dimensions (n ≥ 3) for large μ > 0 in [22] and [38].”
Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities (2022, background): “…concerned with basic solution theories for the corresponding chemotaxis-production version of (1) [5–10], as well as some close variants [11–18,35 In comparison to this, the corresponding chemotaxis-consumption counterpart, as given by appears to exhibit a significantly weaker tendency toward…”