Existence of fast positive wavefronts for a non-local delayed reaction diffusion equation

摘要

We establish the existence of a continuous family of fast positive wavefronts u.t; x/ D .xCct/, .1/ D 0, .C1/ D , for the non-local delayed reactiondiffusion equation ut .t; x/ D uxx.t; x/ u.t; x/ C R K.x w/g.u.t h;w//dw. Here 0 and > 0 are fixed points of g 2 C2.RC; RC/ and the non-negative K is such that RR K.w/ewdw is finite for every real .Wealso prove that the fast wavefronts are non-monotone if g0./hehC1 < 1