Global convergence in a reaction-diffusion equation with piecewise constant argument
In this paper, we consider the reaction-diffusion equation with piecewise constant argument partial derivativeu/partial derivativet =ru(x, t) (1 - u(x,t)) - Eu(X, [t])u(X, t) + D del (2) u on a finite domain, with r, E, D > 0. By employing the method of sub- and super-solutions we prove that, under the condition E < r(1 - exp(-r)), all solutions with positive initial data converge to the positive uniform state. (C) 2001 Elsevier Science Ltd. Ail rights reserved.
reaction-diffusion equations piecewise constant argument comparison principle