In this paper, we establish the maximum norm estimates of the solutions of the finite volume element method （FVE） based on the P1 conforming element for the non-selfadjoint and indefinite elliptic problems.
In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under m...In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption.展开更多
In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spe...In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.展开更多
In this paper, we derive an upper bound estimate of the blow-up rate for positive solutions of indefinite parabolic equations from Liouville type theorems. We also use moving plane method to prove the related Liouvill...In this paper, we derive an upper bound estimate of the blow-up rate for positive solutions of indefinite parabolic equations from Liouville type theorems. We also use moving plane method to prove the related Liouville type theorems for semilinear parabolic problems.展开更多
We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of re...We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes(SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form.展开更多
This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stoc...This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic(LQ)control problems.Second,in order to obtain Nash equilibrium strategies,crosscoupled stochastic Riccati differential(algebraic)equations(CSRDEs and CSRAEs)are derived.Moreover,in order to demonstrate the validity of the obtained results,stochastic H2/H∞control with state-and control-dependent noise is discussed as an immediate application.Finally,a numerical example is provided.展开更多
基金The Major State Basic Research Program (19871051) of China and the NNSP (19972039) of China.
文摘In this paper, we establish the maximum norm estimates of the solutions of the finite volume element method （FVE） based on the P1 conforming element for the non-selfadjoint and indefinite elliptic problems.
基金The Major State Basic Research Program (19871051) of China the NNSF (19972039) of China and Yantai University Doctor Foundation (SX03B20).
文摘In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption.
基金Supported by the National Natural Science Foundation of China(11171152)the Jiangsu Natural Science Foundation of China(BK2010489)
文摘In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.
文摘In this paper, we derive an upper bound estimate of the blow-up rate for positive solutions of indefinite parabolic equations from Liouville type theorems. We also use moving plane method to prove the related Liouville type theorems for semilinear parabolic problems.
基金supported by National Natural Science Foundation of China (Grant Nos. 61573217,11471192 and 11626142)the National High-Level Personnel of Special Support Program,the Chang Jiang Scholar Program of Chinese Education Ministry+2 种基金the Natural Science Foundation of Shandong Province (Grant Nos. JQ201401 and ZR2016AB08)the Colleges and Universities Science and Technology Plan Project of Shandong Province (Grant No. J16LI55)the Fostering Project of Dominant Discipline and Talent Team of Shandong University of Finance and Economics
文摘We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes(SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form.
基金supported by the National Natural Science Foundation of China(No.71171061)China Postdoctoral Science Foundation(No.2014M552177)+2 种基金the Natural Science Foundation of Guangdong Province(No.S2011010004970)the Doctors Start-up Project of Guangdong University of Technology(No.13ZS0031)the 2014 Guangzhou Philosophy and Social Science Project(No.14Q21).
文摘This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic(LQ)control problems.Second,in order to obtain Nash equilibrium strategies,crosscoupled stochastic Riccati differential(algebraic)equations(CSRDEs and CSRAEs)are derived.Moreover,in order to demonstrate the validity of the obtained results,stochastic H2/H∞control with state-and control-dependent noise is discussed as an immediate application.Finally,a numerical example is provided.
