Existence of bounded global solutions for fully parabolic attraction-repulsion

This article concerns the parabolic attraction-repulsion chemotaxis system with  signal-dependent sensitivities $$\displaylines{ u_t=\Delta u-\nabla \cdot (u\chi(v)\nabla v) +\nabla \cdot (u\xi(w)\nabla w), \quad x \in \Omega,\; t>0, \cr v_t=\Delta v-v+u, \quad x \in \Omega,\; t>0, \cr w_t=\Delta w-w+u, \quad x \in \Omega,\; t>0 }$$ under homogeneous Neumann boundary conditions and initial conditions, where \(\Omega \subset \mathbb{R}^n\)  \((n \ge 2)$\) is a bounded domain with smooth boundary, \(\chi, \xi\) are functions satisfying certain conditions. Existence of bounded global classical solutions to the system with logistic source and logistic damping have been obtained in [1]. This article establishes the existence of global bounded classical solutions with logistic damping. For more information see https://ejde.math.txstate.edu/Volumes/2021/71/abstr.html