We construct global generalized solutions to the chemotaxis system ut = ∆u − ∇ • (u∇v) + λ(x)u − µ(x)u κ , vt = ∆v − v + u in smooth, bounded domains Ω ⊂ R n , n ≥ 2, for certain choices of λ, µ and κ. Here, inter alia, the selections µ(x) = |x| α with α < 2 and κ = 2 as well as µ ≡ µ 1 > 0 and κ > min{ 2n−2 n , 2n+4 n+4 } are admissible (in both cases for any sufficiently smooth λ). While the former case appears to be novel in general, in the two-and threedimensional setting, the latter improves on a recent result by Winkler (Adv. Nonlinear Anal. 9 (2019), no. 1, 526-566), where the condition κ > 2n+4 n+4 has been imposed. In particular, for n = 2, our result shows that taking any κ > 1 suffices to exclude the possibility of collapse into a persistent Dirac distribution.

No abstract

No abstract