In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on...In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators(when it exists).The last section of this work is devoted to the properties of the leading eigenvalue(when it exists).So,we discuss the irreducibility of the semigroups generated by these operators.We close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.展开更多
In neutron transport theory, the strict dominance of the dominant eigenvalue associated with the transport operator plays a key role in studying the asymptotic behavior of the time dependent transport system. For boun...In neutron transport theory, the strict dominance of the dominant eigenvalue associated with the transport operator plays a key role in studying the asymptotic behavior of the time dependent transport system. For bounded convex medium surrounded by vacuum, and with energy bounded away from the origin, this problem has been solved. Nevertheless, the result is only obtained under special conditions for nonhomogeneous medium with (0, v_m] energy. The general case will be discussed in this note. By the inequality given in Lemma 3, some hypotheses of [2] are weakened.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
文摘In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators(when it exists).The last section of this work is devoted to the properties of the leading eigenvalue(when it exists).So,we discuss the irreducibility of the semigroups generated by these operators.We close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.
基金Project supported by the National Natural Science Foundation of China.
文摘In neutron transport theory, the strict dominance of the dominant eigenvalue associated with the transport operator plays a key role in studying the asymptotic behavior of the time dependent transport system. For bounded convex medium surrounded by vacuum, and with energy bounded away from the origin, this problem has been solved. Nevertheless, the result is only obtained under special conditions for nonhomogeneous medium with (0, v_m] energy. The general case will be discussed in this note. By the inequality given in Lemma 3, some hypotheses of [2] are weakened.
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.
