Time asymptotic behaviour for a one-velocity transport operator with Maxwell boundary condition (Q2385162)

The author investigates the spectrum of a one-velocity transport operator in a homogeneous medium with the spherical symmetry and Maxwell boundary condition in \(L^1\) space. After a detail spectral analysis, he gets expressions of boundary operator and streaming operator. Using these expressions, he proves that the streaming operator generates a \(C_0\)-semigroup in \(L^1\) space. Using perturbation theory, he shows that the transport operator also generates a \(C_0\)-semigroup. Furthermore, he proves that the transport semigroup is irreducible. Finally, he decomposes the solution of the transport problem into an asymptotic term and a transient one which can be estimated for smooth initial data.