In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary no...In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary nonhomogeneous medium possibly with cavity,withthe anisotropic scattering and fission,and with continuous energy varying from null to any finiteconstant or from one positive constant to another positive constant.We prove that the correspon-ding neutron transport operator A has finite Spectrum points in any strip {λ|β<sub>1</sub>≤R（?）λ≤β<sub>2</sub>}whereβ<sub>2</sub>】β1】-λ<sup>*</sup>（λ<sup>*</sup> is the essential infimum of v∑（x,v））,and obtain the asymptotic expansion ofthe time-dependent solution which exists and is unique.Furthermore,we give the existence ofthe dominant eigenvalue and indicate the asymptotic behavior of the neutron density as t→+∞.展开更多
In this paper, we consider the time dependent neutron transport system concerning a bounded convex medium in R3 with continuous energy and antisotropic scattering and fission.Under the condition of n(r,v) we prove tha...In this paper, we consider the time dependent neutron transport system concerning a bounded convex medium in R3 with continuous energy and antisotropic scattering and fission.Under the condition of n(r,v) we prove that the solution of the system is exponentially stable.展开更多
The well-posedness for the time-dependent neutron transport equationwith integral boundary conditions is established in L^1 space. Some spectral propertiesof the transport operator are discussed, the dominant eigenval...The well-posedness for the time-dependent neutron transport equationwith integral boundary conditions is established in L^1 space. Some spectral propertiesof the transport operator are discussed, the dominant eigenvalue is proved existing,and furthermore, the conservative law of migrating particle numbers is established.展开更多
This paper is devoted to investigating neutron transport in nonhomogeneous slab with generalized boundary conditions and anisotropic scattering-fission kernel. The time dependent equation and the corresponding transpo...This paper is devoted to investigating neutron transport in nonhomogeneous slab with generalized boundary conditions and anisotropic scattering-fission kernel. The time dependent equation and the corresponding transport operator A are discussed in the space of continuous functions. Some aspects of the spectral properties of A (e.g.,the properties of Pas(A) and the dominant eigenvalue of A, etc.) are considered and the exist ence- unique nes s of t he of as s ical t line dep endent so lut ion is obt anied. Furl hermore, an asymptotic expansion (under the maximum norm) of the time dependent solution is givenand the asymptotic behavior is studied.展开更多
基金This work is supported by the National Natural Science Foundation of China
文摘In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary nonhomogeneous medium possibly with cavity,withthe anisotropic scattering and fission,and with continuous energy varying from null to any finiteconstant or from one positive constant to another positive constant.We prove that the correspon-ding neutron transport operator A has finite Spectrum points in any strip {λ|β<sub>1</sub>≤R（?）λ≤β<sub>2</sub>}whereβ<sub>2</sub>】β1】-λ<sup>*</sup>（λ<sup>*</sup> is the essential infimum of v∑（x,v））,and obtain the asymptotic expansion ofthe time-dependent solution which exists and is unique.Furthermore,we give the existence ofthe dominant eigenvalue and indicate the asymptotic behavior of the neutron density as t→+∞.
文摘In this paper, we consider the time dependent neutron transport system concerning a bounded convex medium in R3 with continuous energy and antisotropic scattering and fission.Under the condition of n(r,v) we prove that the solution of the system is exponentially stable.
文摘The well-posedness for the time-dependent neutron transport equationwith integral boundary conditions is established in L^1 space. Some spectral propertiesof the transport operator are discussed, the dominant eigenvalue is proved existing,and furthermore, the conservative law of migrating particle numbers is established.
文摘This paper is devoted to investigating neutron transport in nonhomogeneous slab with generalized boundary conditions and anisotropic scattering-fission kernel. The time dependent equation and the corresponding transport operator A are discussed in the space of continuous functions. Some aspects of the spectral properties of A (e.g.,the properties of Pas(A) and the dominant eigenvalue of A, etc.) are considered and the exist ence- unique nes s of t he of as s ical t line dep endent so lut ion is obt anied. Furl hermore, an asymptotic expansion (under the maximum norm) of the time dependent solution is givenand the asymptotic behavior is studied.
