This paper deals with the global boundedness of solutions to the forager-exploiter model with logistic sources
$ \begin{equation*} \left\{ \begin{array}{lll} u_t = \Delta u- \nabla\cdot(u\nabla w) + \mu_1 (u-u^m), &x \in \Omega, t>0,\\ v_t = \Delta v - \nabla\cdot(v\nabla u) + \mu_2 ( v-v^l), &x\in \Omega, t>0,\\ w_t = \Delta w - \lambda(u+v)w - \mu w + r(x,t), & x\in \Omega, t>0, \end{array} \right. \end{equation*} $
under homogeneous Neumann boundary conditions in a smoothly bounded domain $ \Omega \subset R^2 $, where the constants $ \mu $, $ \mu_1 $, $ \mu_2 $, $ \lambda $, $ m $ and $ l $ are positive. We prove that the corresponding initial-boundary value problem possesses a global classical solution that is uniformly bounded under conditions $ 2\leq m < 3 $, $ l \geq 3 $, $ r(x,t) \in C^1(\overline{\Omega}\times[0,\infty))\cup L^{\infty}(\Omega\times(0,\infty)) $ and the smooth nonnegative initial functions, which improves the results obtained by Wang and Wang (MMMAS 2020).
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