} { \int _{{{{\bf}R}}_+} \!\int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\!\!\!\!\eta (t) { (\alpha - \beta |v|^0) v}\cdot \nabla _v \varphi { f ^{\varepsilon _k}}(t,x,v)\,{ \mathrm{d}(x,v)}&\;\mathrm{d}t}