When do Keller-Segel systems with heterogeneous logistic sources admit generalized solutions?

Jianlu Yan, Mario Fuest

We construct global generalized solutions to the chemotaxis system \begin{align*} \begin{cases} u_t = Δu - \nabla \cdot (u \nabla v) + λ(x) u - μ(x) u^κ,\\ v_t = Δv - v + u \end{ca…