A boundary matching micro/macro decomposition for kinetic equations (Q533996)

The authors consider the following transport equation \[ \varepsilon\partial_tf+v\cdot\nabla_xf=\tfrac{1}{\varepsilon}Lf,\quad t>0,\;(x,v\in\Omega)\times V,\quad f|_{t=0}=f_{\text{init}}, \] where \(f\) is the distribution function of the particles that depends on time \(t>0,\) on position \(x\in\Omega,\) and on velocity \(v\in V.\) The linear operator \(L\) acts on the velocity dependence of \(f.\) The aim is to develop a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions. The idea is to decompose the distribution function \(f\) in its domain as the sum of a Maxwellian part adapted to the boundary and reminder kinetic part.