On the behaviour at infinity of solutions to stationary convection-diffusion equationin a cylinder
Iryna Pankratova, Andrey Lvovich Piatnitski · Discrete and Continuous Dynamical Systems - B · 2009
The work focuses on the behaviour at infinity ofsolutions to second order elliptic equation with first order termsin a semi-infinite cylinder. Neumann's boundarycondition 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.