The Asymptotic Behavior for the Transport Operator in Slab Geometry

Abstract

This paper is devoted to the properties of the generated semigroup by the transport operator in slab geometry with general boundary conditions defined by means of a boundary operator. Under some suitable hypothesis we show that the transport operator generates a strongly continuous semigroup and study its positivity and irreducibility. We also give the asymptotic behavior of the generated semigroup in the operator norm topology.

Keywords:

• Transport operator
• General boundary condition
• Positive and irreducible C ₀–semigroups
• Compactness
• Asymptotic behavior

1991 Mathematics Subject Classification:

• Primary 47D06

Acknowledgments

The author wishes to thank J. Y. Chamard for his help. This research was supported by LMCM-RMI.