Global solutions of a forager–exploiter model with nonlinear diffusions.

This paper is concerned with a doubly tactic resource consumption model with nonlinear diffusions: u t = ∇ · ((u + 1) h - 1 ∇ u) - ∇ · (u ∇ w) , v t = ∇ · ((v + 1) l - 1 ∇ v) - ∇ · (v ∇ u) , w t = Δ w - (u + v) w - w + r (x , t) , where r is a nonnegative bounded function. This system describes the so-called forager–exploiter interaction. It is shown that if h ≥ 2 - 1 / n and l ≥ 2 , then the system has a global weak solution; if in addition min 1 + 1 / n + (h - 2) + , 1 / n + l - 1 > n / 4 + 1 / 2 , then the system has a unique global classical solution. [ABSTRACT FROM AUTHOR]