Homogenization of convection-diffusion equation in infinite cylinder

Iryna Pankratova; Andrey Piatnitski; Iryna Pankratova; Andrey Piatnitski

doi:10.3934/nhm.2011.6.111

Networks and Heterogeneous Media

2011, Volume 6, Issue 1: 111-126. doi: 10.3934/nhm.2011.6.111

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Homogenization of convection-diffusion equation in infinite cylinder

Iryna Pankratova ^{1
,},
Andrey Piatnitski ^{2
,}

1.
Narvik University College, Postbox 385, 8505 Narvik
2.
Narvik University College, HiN, Postbox 385, 8505 Narvik, Norway, and, P.N. Lebedev Physical Institute RAS, Leninski prospect, 53, Moscow, 117924

Received: 01 February 2010 Revised: 01 May 2010
Primary: 35B27, 35B40, 35K20; Secondary: 35B25.

The paper deals with a periodic homogenization problem for a non-stationary convection-diffusion equation stated in a thin infinite cylindrical domain with homogeneous Neumann boundary condition on the lateral boundary. It is shown that homogenization result holds in moving coordinates, and that the solution admits an asymptotic expansion which consists of the interior expansion being regular in time, and an initial layer.
- Homogenization,
- convection-diffusion equation,
- infinite cylinder,
- asymptotic behaviour
Citation: Iryna Pankratova, Andrey Piatnitski. Homogenization of convection-diffusion equation in infinite cylinder[J]. Networks and Heterogeneous Media, 2011, 6(1): 111-126. doi: 10.3934/nhm.2011.6.111

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Abstract

The paper deals with a periodic homogenization problem for a non-stationary convection-diffusion equation stated in a thin infinite cylindrical domain with homogeneous Neumann boundary condition on the lateral boundary. It is shown that homogenization result holds in moving coordinates, and that the solution admits an asymptotic expansion which consists of the interior expansion being regular in time, and an initial layer.

References

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