Entire solution in cylinder-like domains for a bistable   reaction-diffusion equation
  We construct nontrivial entire solutions for a bistable reaction-diffusion equation in a class of domains that are unbounded in one direction. The motivation comes from recent results of Berestycki, Bouhours, and Chapuisat concerning propagation and blocking phenomena in infinite domains. A key assumption in their study was the "cylinder-like" assumption: their domains are supposed to be straight cylinders in a half space. The purpose of this paper is to consider domains that tend to a straight cylinder in one direction.   We also prove the existence of an entire solution for a one-dimensional problem with a non-homogeneous linear term. 
Antoine Pauthier
math.AP