Normalized velocity-reset collision operator
= Normalized velocity-reset collision operator
{title2=$Bg=\rho(g)M-g$}
Let $M\geq0$ have velocity <integral> one, and $\rho(g)(x)=\int g(x,v)dv$. On phase-space $L^1$, the normalized relaxation collision operator is $B=P-I$, where $Pg=\rho(g)M$. It obeys $\|B\|\leq2$ because $\|Pg\|_1\leq\|g\|_1$. It preserves mass at each spatial position. The corresponding <linear Boltzmann equation> combines this bounded collision operator with the <free-transport semigroup>.