Entire solutions in reaction-advection-diffusion equations in cylinders

This paper is concerned with the existence of entire solutions of a reaction-advection-diffusion equation with monostable and ignition temperature nonlinearities in infinite-cylinders. Here the entire solutions are defined in the whole infinite cylinder and for all time t is an element of R. A comparison argument is used to prove the existence of entire solutions which behave as two traveling wave fronts coming from both directions. The main techniques are to characterize the asymptotic behavior of the solutions as t -> -infinity in term of appropriate subsolutions and supersolutions. In order to illustrate our main results, a passive-reaction-diffusion equation model arising from propagation of fronts is considered. This is probably the first time the existence of entire solutions of reaction-diffusion equations in infinite-cylinders has been studied. (c) 2008 Elsevier Masson SAS. All rights reserved.