Asymptotic behaviour of transport equations

Abstract

We take another look at some linear problems of periodic homogenisation of transport type equations, considered recently by different authors. These equations link two space scales, namely the slow macroscopic one, and the fast one, lying on the n-dimensional torus. We present a direct way to get the homogenised equations, involving both scales. In some cases, we are able to get the averaged equations, and this leads to memory effects.

Keywords:

• Ergodicity
• effective equations
• flow on torus
• homogenization
• memory effects