Abstract
We consider the abstract time-dependent linear transport equation as an initial-boundary value evolution problem in the Banach spaces L p , 1 ⩽ p < ∞, or on a space of measures on a (possibly time-dependent) kinetic phase space. Existence, uniqueness, dissipativity, and positivity results are proved for very general, possibly time-dependent, transport operators and boundary conditions. When the phase space, boundary conditions, and transport operator are independent of time, corresponding results are obtained for the associated semigroup.
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