Global existence for a class of chemotaxis-consumption systems with signal-dependent motility and generalized logistic source. (December 2020) - Lv, Wenbin
Abstract: In this paper, we study a chemotaxis-consumption system with signal-dependent motility and generalized logistic source in a smooth bounded domain. We show that if α > 0, ρ ∈ R, μ > 0 and l > max n + 2 2, 2, then for all sufficiently smooth initial data the system u t = Δ ( u v − α ) + ρ u − μ u l, x ∈ Ω, t > 0, v t = Δ v − u v, x ∈ Ω, t > 0, possesses a unique global-in-time solution.