Abstract
We prove the well-posedness of the Cauchy problem governed by a linear mono-energetic singular transport equation (i.e., transport equation with unbounded collision frequency and unbounded collision operator) with specular reflecting and periodic boundary conditions on L p spaces. The large time behaviour of its solution is also considered. We discuss the compactness properties of the second-order remainder term of the Dyson–Phillips expansion for a large class of singular collision operators. This allows us to evaluate the essential type of the transport semigroup from which the asymptotic behaviour of the solution is derived.
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