Classical solutions to a logistic chemotaxis model with singular sensitivity and signal absorption

Abstract

Assuming that 0<χ<2n, κ≥0 and μ>n−22n, we prove global existence of classical solutions to a chemotaxis system slightly generalizing ut=Δu−χ∇⋅(uv∇v)+κu−μu2vt=Δv−uvin a bounded domain Ω⊂Rn, with homogeneous Neumann boundary conditions and for widely arbitrary positive initial data. In the spatially one-dimensional setting, we prove global existence and, moreover, boundedness of the solution for any χ>0, μ>0, κ≥0.