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

Abstract

We study a forager-exploiter model with nonlinear diffusions{ut=∇⋅((u+1)m∇u)−∇⋅(u∇w),vt=∇⋅((v+1)l∇v)−∇⋅(v∇u),wt=Δw−(u+v)w−μw+r in a smooth bounded domain Ω∈Rn with homogeneous Neumann boundary conditions, where μ>0 and r is a given nonnegative function. We prove that, ifm≥1andl∈[1,∞)∩(n(n+2)2(n+1),∞), then the classical solution exists globally and remains bounded.