Geodesic
Generalized Solution of the Photon Transport Problem
Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 28-38

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2010-089-6
Mots-clés : 35K30, 47D03, photon transport, C 0-semigroup 
Chang, Yu-Hsien; Hong, Cheng-Hong. Generalized Solution of the Photon Transport Problem. Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 28-38. doi: 10.4153/CMB-2010-089-6
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[1] [1] Choe, Y. H., C -semigroups on a locally convex space. J.Math. Anal. Appl. 106(1985), no. 2, 293–320. doi:10.1016/0022-247X(85)90115-5 Google Scholar

[2] [2] deLaubenfels, R., Existence families, functional calculi and evolution equations. Lecture Notes in Mathematics, 1570, Springer-Verlag, Berlin, 1994. Google Scholar

[3] [3] Komura, T., Semigroups of operators in locally convex spaces. J. Functional Analysis 2(1968), 258–296. doi:10.1016/0022-1236(68)90008-6 Google Scholar

[4] [4] Köthe, G., Topological vector spaces. II. Grundlehren der Mathematischen Wissenschaften, 237, Springer-Verlag, New York-Berlin, 1979. Google Scholar

[5] [5] Lisi, M. and Totaro, S., Photon transport with a localized source in locally convex spaces. Math Methods Appl. Sci. 29(2006), no. 9, 1019–1033. doi:10.1002/mma.713 Google Scholar

[6] [6] Lisi, M. and Totaro, S., Inverse problems related to photon transport in an interstellar cloud. Transport Theory Statist. Phys. 32(2003), no. 3–4, 327–345. doi:10.1081/TT-120024767 Google Scholar

[7] [7] Teixeira, E. V., Strong solutions for differential equations in abstract spaces. J. Differential Equations 214(2005), no. 1, 65–91. doi:10.1016/j.jde.2004.11.006 Google Scholar

[8] [8] Trèves, F., Topological vector spaces, distributions and kernels. Academic Press, New York-London, 1967. Google Scholar

[9] [9] Yosida, K., “Functional analysis,” Academic Press, New York, 1968 Second Edition. Google Scholar

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