- journal article metadata
European Mathematical Society Publishing House
2017-11-20 23:40:01
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
33
2017
4
On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder
Grégoire
Allaire
Ecole Polytechnique, Palaiseau, France
Andrey
Piatnitski
The Arctic University of Norway, Narvik, Norway
Convection-diffusion, homogenization, boundary layer, effective drift
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.
Partial differential equations
Fluid mechanics
Optics, electromagnetic theory
1123
1148
10.4171/RMI/965
http://www.ems-ph.org/doi/10.4171/RMI/965
11
17
2017