Revista Matemática Iberoamericana


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Volume 33, Issue 4, 2017, pp. 1123–1148
DOI: 10.4171/RMI/965

Published online: 2017-11-17

On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder

Grégoire Allaire[1] and Andrey Piatnitski

(1) Ecole Polytechnique, Palaiseau, France

This paper studies the asymptotic behaviour of the principal eigenfunction of the adjoint Neumann problem for a convection diffusion operator defined in a long cylinder. The operator coefficients are 1-periodic in the longitudinal variable. Depending on the sign of the so-called longitudinal drift (a weighted average of the coefficients), we prove that this principal eigenfunction is equal to the product of a specified periodic function and of an exponential, up to the addition of fast decaying boundary layer terms.

Keywords: Convection-diffusion, homogenization, boundary layer, effective drift

Allaire Grégoire, Piatnitski Andrey: On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder. Rev. Mat. Iberoamericana 33 (2017), 1123-1148. doi: 10.4171/RMI/965