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

• Grégoire Allaire ^[1] ; Andrey Piatnitski ^[2]
  1. [1] University of Paris-Saclay

     University of Paris-Saclay

     Arrondissement de Palaiseau, Francia

     
  2. [2] Narvik University College
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 4, 2017, págs. 1123-1148
• Idioma: inglés
• DOI: 10.4171/RMI/965
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• Resumen

  • 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.