Abstract
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 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 Lp, 1<p< + ∞ For time independent data the transport operator is shown to generate a Co-semigroup on Lp(Σdμ). The results are proven by generalizing a recently established theory of time dependent kinetic equations where the external force is divergence free with respect to velocity. Solutions on spaces of measures are discussed briefly.
Published Version
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