Stability Of Essential Spectrum For Singular Transport Equations With General Boundary Conditions

Under using multiply modern analytical methods, such as spectral theory of operators and the Miyadera perturbation theory of C0 semigroup, this paper has discussed, on Lp(1<p<∞)space,the well-posedness of singular neutron transport equations with anisotropic and nonhomogeneous in slab geometry as well as the related spectral properties with general boundary conditions. In detail,we have turned the singular transport equations into abstract Cauchy problem on Lp(1<p<∞)space and obtained the solution semigroup to prove the well-posedness of solution according to the theory of semigroups; On the basis of Miyadera-Voigt perturbation theory, we give the Dyson-Phillips expansion, then discuss the compactness of Rk(t)by using the method of measure convolution operators, so we can derive the stability of essential spectrum in transport model i.e. the stability of essential spectrum of perturbation semigroup.