Large time behavior to a chemotaxis–consumption model with singular sensitivity and logistic source

Abstract

This paper studies the chemotaxis–consumption model with singular sensitivity and logistic source under homogenous Neumann boundary condition in a smooth bounded domain , with positive parameters χ, ϵ, μ, and f(u) ≃ uα, g(u) ≃ uβ for and β > 0. It is shown that the system possesses a global classical solution when α < 1 and . Furthermore, the asymptotic behavior of solutions is determined for 0 < α < 1 and 0 < β < α in a two‐dimensional setting, provided a sufficiently large μ.