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

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  • 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.
    Mathematics Subject Classification: Primary: 35B40, 35B27, 35J25; Secondary: 76M50.


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