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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

  • 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.

    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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  • 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.


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    [9] I. Pankratova and A. Piatnitski, On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder, DCDS-B, 11 (2009), 935-970. doi: 10.3934/dcdsb.2009.11.935
    [10] L. Trabucho and J. M. Viaño, Derivation of generalized models for linear elastic beams by asymptotic expansion methods, Applications of multiple scaling in mechanis (Paris, 1986), Rech. Math. Appl., 4, Masson, Paris (1987), 302-315.
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