On the behaviour at infinity of solutions to stationary convectiondiffusion equation in a cylinder

(Communicated by Gregoire Allaire) Abstract. The work focuses on the behaviour at infinity of solutions to second order elliptic equation with first order terms in a semi-infinite cylinder. Neu-mann’s boundary condition is imposed on the lateral boundary of the cylinder and Dirichlet condition on its base. Under the assumption that the coefficients stabilize to a periodic regime, we prove the existence of a bounded solution, its stabilization to a constant, and provide necessary and sufficient condition for the uniqueness. 1. Introduction. Thi