Classical solutions to a logistic chemotaxis model with singular sensitivity and signal absorption. (April 2019) - Lankeit, Elisa; Lankeit, Johannes
Abstract: Assuming that 0 < χ < 2 n, κ ≥ 0 and μ > n − 2 2 n, we prove global existence of classical solutions to a chemotaxis system slightly generalizing u t = Δ u − χ ∇ ⋅ ( u v ∇ v ) + κ u − μ u 2 v t = Δ v − u v in a bounded domain Ω ⊂ R n, 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 .