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
This paper deals with a nonlinear initial boundary values problem derived from a modified version of the so called Lebowitz and Rubinow’s model [16] discussed in [8, 9]modeling a proliferating age structured cell pop...This paper deals with a nonlinear initial boundary values problem derived from a modified version of the so called Lebowitz and Rubinow’s model [16] discussed in [8, 9]modeling a proliferating age structured cell population with inherited properties. We give existence and uniqueness results on appropriate weighted L~p-spaces with 1 ≤ p < ∞ in the case where the rate of cells mortality σ and the transition rate k are depending on the total density of population. General local and nonlocal reproduction rules are considered.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.
文摘This paper deals with a nonlinear initial boundary values problem derived from a modified version of the so called Lebowitz and Rubinow’s model [16] discussed in [8, 9]modeling a proliferating age structured cell population with inherited properties. We give existence and uniqueness results on appropriate weighted L~p-spaces with 1 ≤ p < ∞ in the case where the rate of cells mortality σ and the transition rate k are depending on the total density of population. General local and nonlocal reproduction rules are considered.
