The Spectral Mapping Theorem And The Stability Of The Critical Spectrum In Transport Theory

By using the method of function analysis to solve the integro-differential equation, the spectrum analysis is a core and difficult problem in constructing the solution of the equa-tion. In this paper, some problems in transport theory are studied, in detail:The spectral mapping theorem in transport model with zero-reentry boundary condition is discussed, and this is an application to the theory of critical spectrum; The stability of critical spec-trum is proved in transport model with bounce-back boundary condition. At last, some open problems are provided and discussed for further study.