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We study the following Keller-Segel chemotaxis system with logistic sourceand nonlinear secretion: \begin{align*}  u_t=\Delta u- \nabla\cdot(u\nablav)+\kappa(|x|)u-\mu(|x|)u^p\quad\text{and}\quad  0=\Delta v-v+u^\gamma, \end{align*} where$\kappa(\cdot),~\mu(\cdot):[0,R]\rightarrow [0,\infty)$, $\gamma\in(1,\infty)$, $p\in(\gamma+1,\infty)$ and $\Omega \subset \mathbb{R}^n, n\geq2$. For this system, we prove the global existence of solutions under suitableassumptions on the initial condition and the functions $\kappa(\cdot)$ and$\mu(\cdot).$

Global existence of solutions to Keller-Segel chemotaxis system with heterogeneous logistic source and nonlinear secretion