Global Attractivity and Oscillations in a Nonlinear Impulsive Parabolic Equation with Delay

Global attractivity and oscillatory behavior of the following nonlinear impulsive parabolic differential equation which is a general form of many population models {partial derivative u(t, x)/partial derivative t = Delta u(t,x) - delta u(t,x) + f(u(t - tau,x)), t not equal t(k), u(t(k)(+),x) - u(t(k),x) - g(k)(u(t(k),x)), k is an element of I-infinity, are considered. Some new sufficient conditions for global attractivity and oscillation of the solutions of (*) with Neumann boundary condition are established. These results not only are true but also improve and complement existing results for (*) without diffusion or impulses. Moreover, when these results are applied to the Nicholson's blowflies model and the model of Hematopoiesis, some new results are obtained.