Estimates of solutions of impulsive parabolic equations under Neumann boundary condition

In this paper, we prove the relation v(t) u(t , x) w(t), where u(t , x) is the solution of an impulsive parabolic equations under Neumann boundary condition ∂u(t,x)/∂ν = 0, and v(t) and w(t) are solutions of two impulsive ordinary equations. We also apply these estimates to investigate the asymptotic behavior of a model in the population dynamics, and it is shown that there exists a unique solution of the model which converges to the periodic solution of an impulsive ordinary equation asymptotically.  2003 Elsevier Inc. All rights reserved