Diffusion and homogenization limits with separate scales

Naoufel Ben Abdallah, Marjolaine Puel, Michael S. Vogelius

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider the simultaneous diffusion and homogenization limit of the linear Boltzmann equation in a periodic medium in the regime where the mean free path is much smaller than the lattice constant. The resulting equation is a diffusion equation, with an averaged diffusion matrix that is formally obtained by first performing the diffusion limit and then the homogenization one. The rigorous proof relies on the use of two-scale limits, in combination with an asymptotic expansion of the equilibrium profile in powers of the ratio between the mean free path and the lattice constant.

Original languageEnglish (US)
Pages (from-to)1148-1179
Number of pages32
JournalMultiscale Modeling and Simulation
Issue number4
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


  • Diffusion approximation
  • Kinetic equations
  • Two-scale limits


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