Trace theorems and kinetic equations for non divergence free external forces

For a general class of time dependent linear Boltzmann type equations with (i) an external, non divergence free force terma a ∂u/∂ξ (ii) a collision term which can be written as the difference of a gain term involving a general nonnegative "collision frequencyn h(x,ξ,t) and a loss term involving an arbitrary bounded linear operator J, and (iii) a general boundary operator K which is a (strict) contraction, the method of characteristics and perturbation techniques are used to obtain the well-posed- ness of the initial-boundary value problem, provided the divergence b of a is bounded above. The functional setting is L p , 1