The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this paper.We first show that there exist both continuous and discontinuous stationary solutions.Then a good ...The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this paper.We first show that there exist both continuous and discontinuous stationary solutions.Then a good understanding of the stability of discontinuous stationary solutions is gained under an appropriate condition.In addition,we demonstrate the influences of the diffusion coefficient on stationary solutions.The results we obtained are based on the super-/sub-solution method and the generalized mountain pass theorem.Finally,some numerical simulations are given to illustrate the theoretical results.展开更多
In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses...In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses a negative gradient as steepest direction and seeks for an optimal step size to minimize the residual norm of next iterate. It is shown that the iterative sequence converges unconditionally to the exact solution for any initial guess and that the norm of the residual matrix and error matrix decrease monotonically. Numerical tests are presented to show the efficiency of the proposed method and confirm the theoretical results.展开更多
Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence ...Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced.According to some preliminaries,including well-posedness,basic reproduction number and existence of two equilibria,we obtain the threshold dynamics for the model.We illustrate numerical simulations to verify the above theoretical results,and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.展开更多
This paper considers a multi-state repairable system that is composed of two classes of components,one of which has a priority for repair.First,we investigate the well-posedenss of the system by applying the operator ...This paper considers a multi-state repairable system that is composed of two classes of components,one of which has a priority for repair.First,we investigate the well-posedenss of the system by applying the operator semigroup theory.Then,using Greiner’s idea and the spectral properties of the corresponding operator,we obtain that the time-dependent solution of the system converges strongly to its steady-state solution.展开更多
Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for fi...Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>1.This approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using that.In addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)<1 and linearly stable if R_(c)=1;while V^(0)is unstable if R_(c)>1.展开更多
This paper concerns a global optimality principle for fully coupled mean-field control systems.Both the first-order and the second-order variational equations are fully coupled mean-field linear FBSDEs. A new linear r...This paper concerns a global optimality principle for fully coupled mean-field control systems.Both the first-order and the second-order variational equations are fully coupled mean-field linear FBSDEs. A new linear relation is introduced, with which we successfully decouple the fully coupled first-order variational equations. We give a new second-order expansion of Y^(ε) that can work well in mean-field framework. Based on this result, the stochastic maximum principle is proved. The comparison with the stochastic maximum principle for controlled mean-field stochastic differential equations is supplied.展开更多
In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type...In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.展开更多
In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distributi...In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,respectively.We assume that the underlying risk process is modelled by the classical CramérLundberg model process.Under the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,respectively.Furthermore,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy.We find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.展开更多
This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global...This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11790273,52276028).
文摘The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this paper.We first show that there exist both continuous and discontinuous stationary solutions.Then a good understanding of the stability of discontinuous stationary solutions is gained under an appropriate condition.In addition,we demonstrate the influences of the diffusion coefficient on stationary solutions.The results we obtained are based on the super-/sub-solution method and the generalized mountain pass theorem.Finally,some numerical simulations are given to illustrate the theoretical results.
基金supported by the National Natural Science Foundation of China (No. 12001311)Science Foundation of China University of Petroleum,Beijing (No. 2462021YJRC025)the State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum。
文摘In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses a negative gradient as steepest direction and seeks for an optimal step size to minimize the residual norm of next iterate. It is shown that the iterative sequence converges unconditionally to the exact solution for any initial guess and that the norm of the residual matrix and error matrix decrease monotonically. Numerical tests are presented to show the efficiency of the proposed method and confirm the theoretical results.
基金Supported by the Natural Science Foundation of Shanxi Province(202303021211003)the National Natural Science Foundation of China(12126349,11601293,12361102)the Scientific Plan of Guizhou Province(No.Qian Ke He Jichu-ZK[2021]YiBan002).
文摘Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced.According to some preliminaries,including well-posedness,basic reproduction number and existence of two equilibria,we obtain the threshold dynamics for the model.We illustrate numerical simulations to verify the above theoretical results,and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(No.2022D01C46)National Natural Science Foundation of China(No.11801485)。
文摘This paper considers a multi-state repairable system that is composed of two classes of components,one of which has a priority for repair.First,we investigate the well-posedenss of the system by applying the operator semigroup theory.Then,using Greiner’s idea and the spectral properties of the corresponding operator,we obtain that the time-dependent solution of the system converges strongly to its steady-state solution.
基金partially supported by the National Natural Science Foundation of China(Nos.11901027,11971273and 12126426)the Major Program of the National Natural Science Foundation of China(No.12090014)+4 种基金the State Key Program of the National Natural Science Foundation of China(No.12031020)the Natural Science Foundation of Shandong Province(No.ZR2018MA004)the China Postdoctoral Science Foundation(No.2021M703426)the Pyramid Talent Training Project of BUCEA(No.JDYC20200327)the BUCEA Post Graduate Innovation Project(No.PG2022143)。
文摘Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>1.This approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using that.In addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)<1 and linearly stable if R_(c)=1;while V^(0)is unstable if R_(c)>1.
基金supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2020MA032,ZR2022MA029)National Natural Science Foundation of China(Grant Nos.12171279,72171133).
文摘This paper concerns a global optimality principle for fully coupled mean-field control systems.Both the first-order and the second-order variational equations are fully coupled mean-field linear FBSDEs. A new linear relation is introduced, with which we successfully decouple the fully coupled first-order variational equations. We give a new second-order expansion of Y^(ε) that can work well in mean-field framework. Based on this result, the stochastic maximum principle is proved. The comparison with the stochastic maximum principle for controlled mean-field stochastic differential equations is supplied.
基金supported by the Natural Science Foundation of Guangdong(No.2024A1515010983)the project of Guangdong Province General Colleges and Universities with Special Characteristics and Innovations(No.2022KTSCX150)+2 种基金Zhaoqing Science and Technology Innovation Guidance Project(No.2023040317006)Zhaoqing Institute of Education Development Project(No.ZQJYY2023021)Zhaoqing College Quality Project and Teaching Reform Project(No.zlgc202112).
文摘In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.
基金supported by the National Key R&D Program of China(2022YFA1007900)the National Natural Science Foundation of China(Nos.12271171,12171158,12071147,12001200)+3 种基金the Shanghai Philosophy Social Science Planning Office Project(Grant No.2022ZJB005)the Fundamental Research Funds for the Central Universities(2022QKT001)the State Key Program of National Natural Science Foundation of China(71931004)the Humanity and Social Science Foundation of Ningbo University(XPYB19002)。
文摘In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,respectively.We assume that the underlying risk process is modelled by the classical CramérLundberg model process.Under the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,respectively.Furthermore,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy.We find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.
基金supported by the National Natural Science Foundation of China (Nos. 12171024, 11901025,11971217, 11971020)Academic and Technical Leaders Training Plan of Jiangxi Province (No. 20212BCJ23027)。
文摘This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.
