Global existence and asymptotic stability of solutions to a forager-exploiter model with logistic source

In this paper, we consider the following forager-exploiter system{ u(t) = delta u -chi & nabla; middot (u & nabla;w), x is an element of omega, t > 0,v(t) = delta v - xi & nabla; middot (v & nabla;u) + eta v(1 - v(m-1)), x is an element of omega, t > 0,w(t )= delta w - lambda(u+ v)w - mu w + r(x, t), x is an element of omega, t > 0under homogeneous Neumann boundary conditions in a smooth bounded domain omega subset of R-n(n >= 3), where the parameters chi, xi, eta, lambda, m and mu are positive. It is shown that if m > n/2 + 1 and chi is appropriately small, then for all suitably regular initial data, this system possesses a unique global bounded classical solution. Moreover, when additional hypothesis is imposed on r(x, t), the asymptotic behavior can be investigated.