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# Generalized Solution of the Photon Transport Problem

Published:2010-08-09
Printed: Mar 2011
• Yu-Hsien Chang,
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, R.O.C.
• Cheng-Hong Hong,
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, R.O.C.
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## Abstract

The purpose of this paper is to show the existence of a generalized solution of the photon transport problem. By means of the theory of equicontinuous $C_{0}$-semigroup on a sequentially complete locally convex topological vector space we show that the perturbed abstract Cauchy problem has a unique solution when the perturbation operator and the forcing term function satisfy certain conditions. A consequence of the abstract result is that it can be directly applied to obtain a generalized solution of the photon transport problem.
 Keywords: photon transport, $C_{0}$-semigroup
 MSC Classifications: 35K30 - Initial value problems for higher-order parabolic equations 47D03 - Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}

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