PUSHED TRAVELING FRONTS IN MONOSTABLE EQUATIONS WITH MONOTONE DELAYED REACTION

Artículo de publicación ISIWe study the wavefront solutions of the scalar reaction-di usion equations ut(t; x) = u(t; x)u(t; x)+g(u(th; x)); with monotone reaction term g : R+ ! R+ and h > 0. We are mostly interested in the situation when the graph of g is not dominated by its tangent line at zero, i.e. when the condition g(x) g0(0)x; x 0, is not satis ed. It is well known that, in such a case, a special type of rapidly decreasing wavefronts (pushed fronts) can appear in non-delayed equations (i.e. with h = 0). One of our main goals here is to establish a similar result for h > 0. To this end, we describe the asymptotics of all wavefronts (including critical and non-critical fronts) at 1. We also prove the uniqueness of wavefronts (up to a translation). In addition, a new uniqueness result for a class of nonlocal lattice equations is presented