GLOBAL BOUNDEDNESS OF SOLUTIONS TO THE TWO-DIMENSIONAL FORAGER-EXPLOITER MODEL WITH LOGISTIC SOURCE

This paper deals with the global boundedness of solutions to the forager-exploiter model with logistic sources {u(t) = Delta u - del. (u del w) + mu(1)(u - u(m)), x is an element of Omega, t > 0, v(t) = Delta v - del. (v del u) +mu(2)(v - v(l)), 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 > 0, under homogeneous Neumann boundary conditions in a smoothly bounded domain Omega subset of 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 <= m < 3, l >= 3, r (x ,t) is an element of C-1 ((Omega) over bar x [0, infinity)) boolean OR L-infinity (Omega x (0, infinity)) and the smooth nonnegative initial functions, which improves the results obtained by Wang and Wang (MMMAS 2020).