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

Abstract : This paper studies the asymptotic behaviour of the principal eigen-function 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.
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Submitted on : Tuesday, January 19, 2016 - 2:02:45 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:31 PM
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Grégoire Allaire, Andrey Piatnitski. On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder. 2016. ⟨hal-01258747⟩

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