Asymptotic Stability Of The Solution To An Abstract Cauchy Problem And Application To Transport Theory

In this paper, by using the theory of linear operator and operator semigroup theory, combining with the methods of comparison operator and resolvent operator,we prove the asymptotic stability of solutions to an abstract Cauchy problem under certain conditions. The abstract results are then applied to the study of the asymptotic stability of solutions of a class of inhomogeneous medium transport equation with abstract boundary condition, we also obtain the transport operator’s spectral distribution and the stability of essential spectrum.