Existence and large time behavior for a Keller–Segel model with gradient dependent chemotactic sensitivity

Abstract

The purpose of this paper is to study the chemotaxis growth system $$ \begin{cases} u_t=\Delta u-\nabla \cdot (u|\nabla v|^{p-2}\nabla v)+au-bu^{\alpha},& x\in \Omega ,\, t \gt 0,\\ v_t=\Delta v-v+w,& x\in \Omega ,\, t \gt 0,\\ w_t=\Delta w-w+u,& x\in \Om