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Generalized Solution of the Photon Transport Problem

Published online by Cambridge University Press:  20 November 2018

Yu-Hsien Chang and
Cheng-Hong Hong
Yu-Hsien Chang
Affiliation:
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, R. O. C. e-mail: changyh@math.ntnu.edu.tw hong838@yahoo.com.tw
Cheng-Hong Hong
Affiliation:
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, R. O. C. e-mail: changyh@math.ntnu.edu.tw hong838@yahoo.com.tw
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Abstract

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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

35K3047D03photon transportC 0-semigroup

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 1 , 01 March 2011, pp. 28 - 38
Copyright
Copyright © Canadian Mathematical Society 2011

References

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