LAUSR

Abstract 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.