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June  2009, 11(4): 935-970. doi: 10.3934/dcdsb.2009.11.935

On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder

1. 

Narvik University College, Postbox 385, 8505 Narvik, Norway, Norway

Received  June 2008 Revised  September 2008 Published  April 2009

The work focuses on the behaviour at infinity of solutions to second order elliptic equation with first order terms in a semi-infinite cylinder. Neumann'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.
Citation: Iryna Pankratova, Andrey Piatnitski. On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 935-970. doi: 10.3934/dcdsb.2009.11.935
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