TRAVELING WAVE SOLUTIONS FOR FULLY PARABOLIC KELLER-SEGEL CHEMOTAXIS SYSTEMS WITH A LOGISTIC SOURCE.

This article concerns traveling wave solutions of the fully parabolic Keller-Segel chemotaxis system with logistic source, ... where χ, µ, λ, a, b are positive numbers, and τ ≥ 0. Among others, it is proved that if b > 2χµ and τ ≥ 1/2 (1 - λ/α)+, then for every c ≥ 2√α, this system has a traveling wave solution (u; v)(t; x) = (Uτ,c(x ⋅ξ - ct), Vτ,c (x ⋅ ξ - ct)) (for all ξ ∈ ℝN) connecting the two constant steady states (0; 0) and (a/b, µ/λ, a/b), and there is no such solutions with speed c less than 2√a, which improves the results established in [30], and shows that this system has a minimal wave speed c0* = 2√a, which is independent of the chemotaxis. [ABSTRACT FROM AUTHOR]