Global existence and boundedness of a forager-exploiter system with nonlinear diffusions.

We study a forager-exploiter model with nonlinear diffusions { u t = ∇ ⋅ ((u + 1) m ∇ u) − ∇ ⋅ (u ∇ w) , v t = ∇ ⋅ ((v + 1) l ∇ v) − ∇ ⋅ (v ∇ u) , w t = Δ w − (u + v) w − μ w + r in a smooth bounded domain Ω ∈ R n with homogeneous Neumann boundary conditions, where μ > 0 and r is a given nonnegative function. We prove that, if m ≥ 1 and l ∈ [ 1 , ∞) ∩ (n (n + 2) 2 (n + 1) , ∞) , then the classical solution exists globally and remains bounded. [ABSTRACT FROM AUTHOR]