Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (4): 703-714.

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

Wu Hongxing, Wang Shenghua, Cheng Guofei   

  1. College of Mathematics and Computer Science, Shangrao Normal University, Jiangxi Shangrao 334001
  • Received:2015-12-11 Revised:2016-05-12 Online:2016-08-26 Published:2016-08-26
  • Supported by:

    Supported by the NSFC(11461055,11561057),the Natural Science Foundation of Jiangxi Province(20151BAB201029) and the Science and Technology Project of Education Department of Jiangxi Province(151056)

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
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