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.
Cite this article
Grégoire Allaire, Andrey Piatnitski, On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder. Rev. Mat. Iberoam. 33 (2017), no. 4, pp. 1123–1148DOI 10.4171/RMI/965