Essential spectrum of a transport operator with abstract boundary conditions
WU Hong-xin · Journal of Liaoning Technical University · 2014
In order to obtain the essential spectra of transport operator, the objective of this paper is to discuss the asymptotic behavior of solution to transport equation with anisotropic continuous energy with abstract boundary conditions in slab geometry in 1 L space. It is to prove that the transport operator H A generates a 0 C semigroup and the ninth-order remained term 9 R(t) of the Dyson-Phillps expansion of the 0 C semigroup is weakly compact in 1 L space in the conditions of boundary operator being partly compact and disturbance operator is regular, and it to obtain that semigroup V(t) which is generated by the transport operator and semigroupU(t) which is generated by streaming operator H B have the same essential spectral radius. The paper relies on the theory of operators and comparison operator methods, and so on.