Large time behavior of solutions to parabolic equations with Neumann boundary conditions

In this paper we are interested in the large time behavior as t -> +infinity of the viscosity solutions of parabolic equations with nonlinear Neumann type boundary conditions in connection with ergodic boundary problems which have been recently studied by Barles and the author in [G. Barles, F. Da Lio, On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions, Ann. Inst. H. Poincare Anal. Non Lineaire 22 (5) (2005) 521-541]. (c) 2007 Elsevier Inc. All rights reserved.