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

Grégoire Allaire, Andrey L. Piatnitski

• 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.