Dirichlet Problem for the Diffusive Nicholson's Blowflies Equation

The object of this paper is to consider the asymptotic behavior of solutions of the diffusive Nicholson's blowflies equation under Dirichlet boundary condition. A new approach is developed to study the global attractivity of the positive steady state for a reaction diffusion equation with time delay, when monotone or quasi–monotone conditions fail to apply. This approach should be applicable to other Dirichlet problems as well, even though our analysis is tailored to the diffusive Nicholson's blowflies equation.