This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectrul distribution of system oper...This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectrul distribution of system operator and its quasi-compactness. Some primary reliability indices are discussed with the eigenfunction of system operator and the optimal vacation time to get the maximum system profit is analyzed at the end of paper.展开更多
This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the...This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.展开更多
The reliability of a complex system passes through a gradual deterioration until at some critical level, the system fails completely. The study of the exponential stability of such a system requires the application of...The reliability of a complex system passes through a gradual deterioration until at some critical level, the system fails completely. The study of the exponential stability of such a system requires the application of functional analysis and, particularly, the theory of linear operators in Banach space to demonstrate the existence of strictly dominant eigenvalue. Through analyzing the variation of the essential spectral radius of semigroups before and after perturbation, it is shown that the dynamic solution of the system converges to the steady-state solution of the system exponentially under certain condition.展开更多
Let (X;‖ ‖) be a Banach space. By B(X) we denote the set of all bounded linear operators in X. Let C∈B(X) be injective.A strongly continuous family of bounded operators {S(t); t≥0} is called an exponentially bound...Let (X;‖ ‖) be a Banach space. By B(X) we denote the set of all bounded linear operators in X. Let C∈B(X) be injective.A strongly continuous family of bounded operators {S(t); t≥0} is called an exponentially bounded C-semigroup (hereinafter abbrevi-展开更多
The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are e...The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown.展开更多
By analyzing the spectrum location of system operator of redundant repairable system, this paper proved that the dynamic solutions of the system converge to the steady solution. Moreover, the normalized steady solutio...By analyzing the spectrum location of system operator of redundant repairable system, this paper proved that the dynamic solutions of the system converge to the steady solution. Moreover, the normalized steady solution is just the steady availability of the system.展开更多
In this paper we study transport processes on infinite networks with dynamic boundary control nodes. These flows can be modeled by operator semigroups on a suitable Banach space. Using functional analytical and graph ...In this paper we study transport processes on infinite networks with dynamic boundary control nodes. These flows can be modeled by operator semigroups on a suitable Banach space. Using functional analytical and graph theoretical methods, we investigate its spectral properties of the system and positivity of the semigroup under appropriate assumptions on the network.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11001013
文摘This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectrul distribution of system operator and its quasi-compactness. Some primary reliability indices are discussed with the eigenfunction of system operator and the optimal vacation time to get the maximum system profit is analyzed at the end of paper.
基金This work was supported by grants from NNSF of China(No:10271044)Scientific Research Fund of Educational Department of Anhui Province(NSF2003KJ005zd)Teaching Research Fund of Educational Department of Anhui Province(JYXM2003108).
文摘This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.
文摘The reliability of a complex system passes through a gradual deterioration until at some critical level, the system fails completely. The study of the exponential stability of such a system requires the application of functional analysis and, particularly, the theory of linear operators in Banach space to demonstrate the existence of strictly dominant eigenvalue. Through analyzing the variation of the essential spectral radius of semigroups before and after perturbation, it is shown that the dynamic solution of the system converges to the steady-state solution of the system exponentially under certain condition.
基金Project supported by the National Natural Science Foundation of China.
文摘Let (X;‖ ‖) be a Banach space. By B(X) we denote the set of all bounded linear operators in X. Let C∈B(X) be injective.A strongly continuous family of bounded operators {S(t); t≥0} is called an exponentially bounded C-semigroup (hereinafter abbrevi-
基金the Natural Science Foundation of Henan Province (No.994051200).
文摘The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown.
文摘By analyzing the spectrum location of system operator of redundant repairable system, this paper proved that the dynamic solutions of the system converge to the steady solution. Moreover, the normalized steady solution is just the steady availability of the system.
文摘In this paper we study transport processes on infinite networks with dynamic boundary control nodes. These flows can be modeled by operator semigroups on a suitable Banach space. Using functional analytical and graph theoretical methods, we investigate its spectral properties of the system and positivity of the semigroup under appropriate assumptions on the network.
