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Time Asymptotic Behaviour for a One-Velocity Transport Operator with Maxwell Boundary Condition |
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| Authors: | Aref Jeribi Sid Ahmed Ould Ahmed Mahmoud Ridha Sfaxi |
| Institution: | (1) Département de Mathématiques, Faculté des Sciences, Université de Sfax, Route de Soukra, Km 3.5, B.P. 802, 3018 Sfax, Tunisie;(2) Département de Mathématiques, Faculté des Sciences de Gabès, Université de Gabès, Route de Médenine, 6029 Gabès, Tunisie;(3) Département des Méthodes Quantitatives, Institut Supérieur de Gestion de Gabès, Université de Gabès, Avenue Jilani Habib, 6002 Gabès, Tunisie |
| Abstract: | This paper is concerned with the spectral analysis of a one-velocity transport operator with Maxwell boundary condition in L 1-space. After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C 0-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup is irreducible. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will be estimated for smooth initial data is given. |
| Keywords: | Nuclear reactor theory Neutron transport General spectral theory of PDE Boundary value problems for PsDO |
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