Homogenization of linear and nonlinear transport equations

E. Weinan

Research output: Contribution to journalArticlepeer-review

97 Scopus citations


We study the homogenization of the linear and nonlinear transport equations with oscillatory velocity fields. Two types of homogenized equations are derived. For general n‐dimensional linear and nonlinear problems, we derive homogenized equations by introducing additional independent variables to represent the small scales. For the two‐dimensional linear transport equations, we derive effective equations for the averaged quantities. Such equations take the form of either a degenerate non‐local diffusion equation with memory or a higher order hyperbolic equation. To study the nonlinear transport equations we introduce the concept of two‐scale Young measure and extend DiPerna's method to prove that it reduces to a family of Dirac measures.

Original languageEnglish (US)
Pages (from-to)301-326
Number of pages26
JournalCommunications on Pure and Applied Mathematics
Issue number3
StatePublished - Mar 1992

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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