Linear transport equations in plane-parallel homogeneous media have been studied as abstract boundary value problems on complex Hilbert spaces for three decades [82, 83, 24, 15, 152, 102, 77]. Here we study their evolution operators as multiplicative perturbations of exponentially dichotomous operators, first for multiplicative perturbations that are compact perturbations of the identity, then for positive selfadjoint (bounded as well as unbounded) multiplicative perturbations. We also derive formal solutions of the relevant boundary value problems.
KeywordsTransport Equation Compact Operator Bounded Linear Operator Selfadjoint Operator Unique Solvability
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