# Homogenization of a spectral equation with drift in linear transport

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 6, page 613-627
- ISSN: 1292-8119

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topBal, Guillaume. "Homogenization of a spectral equation with drift in linear transport." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 613-627. <http://eudml.org/doc/197355>.

@article{Bal2010,

abstract = {
This paper deals with the homogenization of a spectral equation
posed in a periodic domain in linear transport theory. The particle
density at equilibrium is given by the unique normalized positive
eigenvector of this spectral equation. The corresponding eigenvalue
indicates the amount of particle creation necessary to reach this
equilibrium. When the physical parameters satisfy some symmetry
conditions, it is known that the eigenvectors of this equation can
be approximated by the product of two term. The first one solves a
local transport spectral equation posed in the periodicity cell and
the second one a homogeneous spectral diffusion equation posed in
the entire domain. This paper addresses the case where these
symmetry conditions are not fulfilled. We show that the
factorization remains valid with the diffusion equation replaced by
a convection-diffusion equation with large drift. The asymptotic
limit of the leading eigenvalue is also modified. The spectral
equation treated in this paper can model the stability of nuclear
reactor cores and describe the distribution of neutrons at
equilibrium. The same techniques can also be applied to the
time-dependent linear transport equation with drift, which appears
in radiative transfer theory and which models the propagation of
acoustic, electromagnetic, and elastic waves in heterogeneous media.
},

author = {Bal, Guillaume},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Homogenization; linear transport; eigenvalue problem; drift.; periodic domain; stability of nuclear reactor cores; linear transport equation with drift; waves in heterogeneous media},

language = {eng},

month = {3},

pages = {613-627},

publisher = {EDP Sciences},

title = {Homogenization of a spectral equation with drift in linear transport},

url = {http://eudml.org/doc/197355},

volume = {6},

year = {2010},

}

TY - JOUR

AU - Bal, Guillaume

TI - Homogenization of a spectral equation with drift in linear transport

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 6

SP - 613

EP - 627

AB -
This paper deals with the homogenization of a spectral equation
posed in a periodic domain in linear transport theory. The particle
density at equilibrium is given by the unique normalized positive
eigenvector of this spectral equation. The corresponding eigenvalue
indicates the amount of particle creation necessary to reach this
equilibrium. When the physical parameters satisfy some symmetry
conditions, it is known that the eigenvectors of this equation can
be approximated by the product of two term. The first one solves a
local transport spectral equation posed in the periodicity cell and
the second one a homogeneous spectral diffusion equation posed in
the entire domain. This paper addresses the case where these
symmetry conditions are not fulfilled. We show that the
factorization remains valid with the diffusion equation replaced by
a convection-diffusion equation with large drift. The asymptotic
limit of the leading eigenvalue is also modified. The spectral
equation treated in this paper can model the stability of nuclear
reactor cores and describe the distribution of neutrons at
equilibrium. The same techniques can also be applied to the
time-dependent linear transport equation with drift, which appears
in radiative transfer theory and which models the propagation of
acoustic, electromagnetic, and elastic waves in heterogeneous media.

LA - eng

KW - Homogenization; linear transport; eigenvalue problem; drift.; periodic domain; stability of nuclear reactor cores; linear transport equation with drift; waves in heterogeneous media

UR - http://eudml.org/doc/197355

ER -

## References

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