一类抽象Cauchy问题解的渐近性态及应用

The Asymptotic Behavior of the Solution of an Abstract Cauchy Problem and Its Applications

算子半群的方法在讨论抽象Cauchy问题的渐近性时是非常有用的。若L生成C_0半群(T(t))_(t≥0),K为有界线性算子,[1]证明了当T(t)及K满足某种条件时,在某条平行于虚轴的直线右边除预解集外全是L+K的有限个具有限代数重数的离散本征值,但条件是加在T(t)上的,

In the paper we discuss the distribution of the discrete eigenvalue with finite algebra multiplicity of a strongly continuous perturbed semigroup and the asymptotic expansion of this semigroup. As the application, the positive solution of the transport equation which is non-isotropic scattering, continue energy, nonhomogeneous bound convex body with generalized reflected boundary condition is well posed and we also get its asymptotic behavior.