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Generalized Solution of the Photon Transport Problem |
Canad. Math. Bull. 54(2011), 28-38
Published:2010-08-09
Printed: Mar 2011
Printed: Mar 2011
- Yu-Hsien Chang,
- Cheng-Hong Hong,
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} |