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.

A particle transport problem with nonhomogeneous reflection boundary conditions / A. Belleni Morante; L. Barletti. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - STAMPA. - 21(11):(1998), pp. 1049-1066. [10.1002/(SICI)1099-1476(19980725)21:11<1049::AID-MMA984>3.0.CO;2-W]

A particle transport problem with nonhomogeneous reflection boundary conditions

BELLENI MORANTE, ALDO;BARLETTI, LUIGI
1998

Abstract

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
21(11)
1049
1066
A. Belleni Morante; L. Barletti
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/314053
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