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

Iryna Pankratova; Andrey Piatnitski

doi:10.3934/dcdsb.2009.11.935

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2009, Volume 11, Issue 4: 935-970. Doi: 10.3934/dcdsb.2009.11.935

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

Iryna Pankratova^1, and
Andrey Piatnitski^1,

1.
Narvik University College, Postbox 385, 8505 Narvik

Received: May 31, 2008

Revised: August 31, 2008

Published: October 2009

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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. 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.

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

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