# Homogenization of linear and nonlinear transport equations

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88 Scopus citations

## Abstract

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 language English (US) 301-326 26 Communications on Pure and Applied Mathematics 45 3 https://doi.org/10.1002/cpa.3160450304 Published - Mar 1992 Yes

## All Science Journal Classification (ASJC) codes

• Mathematics(all)
• Applied Mathematics
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