Global solutions of a doubly tactic resource consumption model with logistic source

We study a doubly tactic resource consumption model (u(t) = & UDelta;u - backward difference & BULL; (u backward difference w), v(t) = & UDelta;v - backward difference & BULL; (v backward difference u) + v(1 - v(beta-1)), w(t) = & UDelta;w - (u + v)w - w + r) in a smooth bounded domain omega & ISIN;R2 with homogeneous Neumann boundary conditions, where r & ISIN;C1(omega x[0,& INFIN;))& AND;L & INFIN;(omega x(0,& INFIN;)) is a given non-negative function fulfilling integral tt+1 integral omega| backward difference r|2 <& INFIN; for all t & GE; 0. It is shown that, first, if beta > 2, then the corresponding Neumann initial-boundary problem admits a global bounded classical solution. Second, when beta = 2, the Neumann initial-boundary problem admits a global generalized solution.