板模型中一类具抽象边界条件的迁移方程 解的渐近稳定性

Abstract

Abstract:

First, the objective of this paper is to discuss the transport equation of anisotropic, continuous energy and inhomogeneous medium with abstract boundary condition in slab geometry. Second, it is to prove that the transport operator generates a C₀ semigroup and the ninth-order remained term of the Dyson-phillips expansion of the C₀ semigroup is weakly compact, and it obtains that the spectrum of the transport operator only consists of finite isolated eigenvalues with a finite algebraic multiplicity in the trip Γ₀. Finally, it discusses the solution of transport equation is asymptotic stability. The paper relies on the theory of linear operators, resolvent operator, and comparison operator methods.

Key words: Transport equation, Abstract boundary condition, Weakly compactness, Discrete eigenvalues, Stability

CLC Number:

O177.2

Wu Hongxing, Wang Shenghua, Cheng Guofei. The Stability of a Transport Equations Solution with Abstract Boundary Condition in Slab Geometry[J].Acta mathematica scientia,Series A, 2016, 36(4): 703-714.

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The Stability of a Transport Equations Solution with Abstract Boundary Condition in Slab Geometry

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