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A particle transport problem with non‐homogeneous reflection boundary conditions
Author(s) -
BelleniMorante A.,
Barletti L.
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19980725)21:11<1049::aid-mma984>3.0.co;2-w
Subject(s) - mathematics , boundary (topology) , homogeneous , affine transformation , boundary value problem , bounded function , regular polygon , reflection (computer programming) , mathematical analysis , pure mathematics , geometry , combinatorics , computer science , programming language
We consider particle transport in a three‐dimensional convex region V , bounded by the regular surface ∂ V . We assume that particles are specularly reflected by ∂ V and that a source q is assigned on ∂ V ; more general non‐homogeneous boundary conditions are also discussed. The problem is non‐linear because the boundary condition is not homogeneous. We prove existence of a unique strict solution and by using the theory of semigroups we derive the explicit expression of such a solution in terms of the boundary source q . In the appendix, we indicate how some properties of affine operators can be used to derive the solution. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.